ORDER

The opinion filed October 10, 1995 is withdrawn.

OPINION

A state court jury found Petitioner-Appel-lee Stokes Ray Crotts guilty of assault with a deadly weapon upon a peace officer in violation of California Penal Code § 245(e). After his conviction was affirmed on direct appeal, Crotts unsuccessfully petitioned the California state courts for a writ of habeas corpus. Crotts then petitioned the United States District Court for habeas relief. The district court granted the petition, ruling that the failure of Crotts’s counsel to object to highly prejudicial testimony, introduced by the prosecution, denied Crotts his right to effective assistance of counsel. Respondent Warden George Smith (the “State”) now appeals.

We have jurisdiction under 28 U.S.C. § 1291 . We affirm.

I. FACTS AND PRIOR PROCEEDINGS

The undisputed facts are as follows: On October 24, 1989, Deputy Sheriffs Schoon-maker and Thanstrom noticed Crotts’s pickup truck parked in a dirt turnout on Lopez Canyon Road, Los Angeles County, California. Sehoonmaker saw a man (Crotts) and a woman (Greeley) in the truck. Sehoonmaker approached the truck and asked Crotts for identification. Crotts handed over a social security card with the name “Shane L. Shaffer.” When Crotts could not recite the number on the card, Sehoonmaker asked Crotts to step out of the truck. As Crotts exited the truck, he picked up a tennis shoe containing a syringe and a plastic aspirin bottle.

Thereafter, the accounts of the witnesses diverge. Sehoonmaker testified that Crotts tried to conceal the shoe and then throw the shoe off the road; Sehoonmaker grabbed Crotts’s arm and took the shoe, and then told Crotts to put his hands on the truck; Crotts then lunged through the open door of the truck and into the driver’s seat, and attempted to reach for the keys in the ignition; Sehoonmaker then hit Crotts’s head with a flashlight; Crotts started the engine; Sehoonmaker hit Crotts on the head again; the truck started forward; Sehoonmaker was halfway in the truck and halfway out; Crotts accelerated the truck, dragging Sehoonmaker along the road; Sehoonmaker grabbed his gun and fired four shots at Crotts; the truck then came to a stop.

Crotts testified at trial that after he exited the truck, Sehoonmaker asked him to place his hands on the truck. As he did so, Crotts felt the truck begin to move, so he reentered the truck and grabbed the steering wheel. Crotts then felt a heavy blow to his head; he lost his vision and then felt a second blow to his head. Crotts then fell unconscious and does not remember anything thereafter.

At trial, the prosecution, in its case in chief, introduced into evidence the fact that Crotts was on parole for an undisclosed felony that he committed in Oregon. Crotts then took the stand in his defense. The prosecution asked him on cross examination whether he told Greeley, the passenger in his truck, that he was wanted for “killing a cop.” Crotts’s counsel did not object to the question. Crotts then replied, “No, Ma’am.”

In fact, it is undisputed that Crotts had never killed a police officer. At oral argument, the prosecutor admitted that he knew when cross examining Crotts that he had committed no such offense.

Towards the end of the trial, this highly prejudicial evidence was again introduced by the prosecution and admitted into evidence. In chambers, the trial judge asked Crotts’s counsel whether he had any objections to the prosecution calling Greeley to testify that Crotts did make the “killing a cop” statement. Again, Crotts’s counsel did not object, stating, “Well, I mean if she’s going to testify that he made these statements, your honor, I think that I’m not going to object to them. I think they are probably relevant.”

Greeley was then called to the stand. She testified, without objection, that Crotts told her that he “had just done ten years for killing a policeman.”

The jury convicted Crotts of assault with a deadly weapon upon a peace officer in violation of California Penal Code § 245(c). In his state habeas proceedings, Crotts alleged that the failure of his trial counsel to object to the prosecutor’s questioning of Greeley regarding the “killing a cop” statement deprived him of his right to effective assistance of counsel and of his Fourteenth Amendment due process rights. In his habeas petition to the California Supreme Court Crotts stated:

Stokes Ray Crotts, Jr., Memorandum of Points and Authorities in Support of Petition for Writ of Habeas Corpus 3-4 (filed March 3, 1994 with the California Supreme Court). The California Supreme Court denied Crotts’s petition on April 27,1994.

On May 20, 1994, Crotts filed a pro se petition for a writ of habeas corpus in the United States District Court for the Central District of California. In his petition, he stated that his Sixth and Fourteenth Amendment rights were violated because he had not received effective assistance of counsel. The magistrate judge recommended granting the petition: The magistrate judge concluded that the failure of Crotts’s trial counsel to object to both the prosecution’s questioning of Greeley and of Crotts regarding the “killing a cop” statement constituted ineffective assistance of counsel. The district judge adopted the magistrate’s recommendation and granted the habeas petition on October 26,1994. The State now appeals.

II. STANDARD OF REVIEW

The decision whether to grant or deny a petition for habeas corpus is reviewed de novo. Calderon v. Prunty, 59 F.3d 1005, 1008 (9th Cir.1995). A claim of ineffective assistance of counsel is a mixed question of law and fact reviewed de novo. Moran v. Godinez, 57 F.3d 690, 699 (9th Cir.1995).

III. DISCUSSION

We review this case, first to determine whether Crotts has exhausted his state remedies for his federal constitutional claims, and then to analyze whether he received constitutionally ineffective assistance of counsel.

A. Exhaustion of State Remedies

The Supreme Court “has long held that a state prisoner’s federal habeas petition should be dismissed if the prisoner has not exhausted available state remedies as to any of his federal claims.” Coleman v. Thompson, 501 U.S. 722, 731 , 111 S.Ct. 2546, 2554 , 115 L.Ed.2d 640 (1991) (citations omitted). The exhaustion-of-state-remedies doctrine, now codified at 28 U.S.C. §§ 2254 (b) and (c), reflects a policy of federal-state comity to give the State “the initial ‘opportunity to pass upon and correct alleged violations of its prisoners’ federal rights.’ ” Picard v. Connor, 404 U.S. 270, 275 , 92 S.Ct. 509, 512 , 30 L.Ed.2d 438 (1971) (citations omitted). Once the federal claim has been “fairly presented” to the state courts, the exhaustion requirement is satisfied. Id.

The Supreme Court.recently restated its Picard exhaustion analysis in Duncan v. Henry, — U.S. -, 115 S.Ct. 887 , 130 L.Ed.2d 865 (1995). The Court explained:

Duncan v. Henry, — U.S. at -, 115 S.Ct. at 888 (citations omitted).

In Duncan v. Henry, petitioner Robert Henry did not apprise the state court of his claim that the trial court’s evidentiary ruling was not just a violation of state law, but also a denial of his Fourteenth Amendment due process rights. Id. at -, 115 S.Ct. at 888 . The Court, therefore, concluded that Henry had not met the exhaustion requirement because he had not alerted the state courts to his federal claim.

Here, by contrast, Crotts meets the Picard-Duncan exhaustion requirement. In his habeas petition to the California Supreme Court, Crotts alleged violations of his rights under the United States Constitution and explicitly alleged violations of his right to effective assistance of counsel and his Fourteenth Amendment due process rights. In particular, Crotts claimed that his counsel was ineffective for failing to object to the presentation of the highly prejudicial “killing a cop” evidence. Thus, the record is clear: California’s courts were alerted to the fact that Crotts was asserting federal constitutional claims in his petition for habeas. Crotts, therefore, meets the exhaustion requirement.

B. Ineffective Assistance of Counsel

In Strickland v. Washington, 466 U.S. 668, 688-693 , 104 S.Ct. 2052, 2064-68 , 80 L.Ed.2d 674 (1984), the Supreme Court established the two requirements that defendants must meet to prevail on a claim of ineffective assistance of counsel: (1) The defendant must show that counsel’s performance fell outside the wide range of professional competence; and (2) the defendant must prove that his trial counsel’s conduct was prejudicial to his case, i.e., that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.”

1. Reasonableness of Counsel’s Performance

It is well established that evidence of a defendant’s prior bad act generally is inad-missable to show that the defendant had the criminal disposition or propensity to commit the crime charged. Cal.Evid.Code § 1101(a). Such evidence is only admissible when relevant to prove a fact other than criminal disposition, such as motive or intent. Cal. Evid.Code § 1101(b). Even then, the evidence is inherently prejudicial and must be excluded if its probative value is substantially outweighed by undue prejudice. Cal.Evid. Code § 352.

In United States v. Bradley, 5 F.3d 1317, 1321 (9th Cir.1993), we recognized the prejudice inherent in admitting evidence of other crimes:

Id. at 1320 (quotations omitted).

The district court correctly concluded that the failure of Crotts’s counsel to object to the prosecution’s questioning of Greeley and of Crotts on the “killing a cop” statement fell outside the wide range of professional competence. The jury learned that Crotts was on parole for an undisclosed felony. Upon hearing the “killing a cop” testimony, it would not take much more for jurors to infer that Crotts had been convicted of killing a police officer when in fact no such offense occurred.

The jury’s likely inference that a person who has killed a police officer is the kind of person who would assault a police officer with a deadly weapon is exactly the kind of propensity-based inference that Cal.Evid. Code § 1101(a) was designed to exclude. Reasonably competent counsel undoubtedly would have objected to the admission of such prejudicial evidence. See People v. Robertson, 33 Cal.3d 21 , 188 Cal.Rptr. 77, 87 , 655 P.2d 279 (1982) (defense counsel ineffective for failing to object to rape victim’s testimony that defendant said he previously killed two women); People v. Guizar, 180 Cal.App.3d 487 , 225 Cal.Rptr. 451, 453 , 454 n. 3 (1986) (defense counsel should have objected to evidence that defendant committed other murders).

The State argues that the “killing a cop” statement was admissible to show motive and intent: The fact that Crotts stated that he had killed a police officer shows that Crotts had the intent to injure Officer Schoonmaker. The State does not explain how an untrue boastful remark about having killed a police officer in the past establishes a present intent to assault a police officer, nor does the record support such a connection.

Moreover, at oral argument, the State’s counsel conceded that the prosecution knew that the statement was untrue, i.e., the prosecution knew that Crotts had never been convicted of killing a police officer. This fact further diminishes any probative value of introducing the statement into evidence.

The State also contends that Crotts’s counsel had tactical reasons for not objecting to the prejudicial testimony. Again, the State’s arguments are specious. It is implausible that a reasonably competent attorney would have dismissed the inflammatory “killing a cop” testimony as harmless “hyperbole.”

2. Prejudice

In addition to showing that his counsel’s performance fell outside the wide range of professional competence, Crotts must show that there is a reasonable probability that, but for his counsel’s ineffectiveness, the result of the proceeding would have been different. See Strickland, supra. The district court correctly concluded that the failure of Crotts’s counsel to object to the “killing a cop” testimony could have altered the outcome of Crotts’s case.

Had Crotts’s counsel objected, it is reasonably certain that the trial judge would have excluded the testimony in question because its probative value was slight and its prejudicial effect great. Indeed, the trial judge signalled to Crotts’s counsel the potentially prejudicial effect of the testimony by asking her, in a separate proceeding in chambers, if she had any objections to the proposed questioning of Greeley.

The State contends that overwhelming evidence of Crotts’s guilt was presented to the jury, which negated any prejudicial effect of the inflammatory testimony. But, as the district court correctly concluded, the prosecution’s case “was less than overwhelming.” The prosecution’s evidence primarily consisted of the police officers’ testimony, which was contradicted by Crotts’s testimony, and to a certain extent, Greeley’s testimony. As such, the ease turned on the credibility of the witnesses. The inflammatory evidence, which no doubt diminished Crotts’s credibility, thus prejudiced Crotts.

The State also argues that any prejudicial effect was cured by Crotts’s denial of having made the statement in question. We disagree. Crotts’s denial was directly refuted by Greeley’s testimony, in which Greeley stated that Crotts did make the statement. But, as just shown above, because the outcome of the ease turned on the credibility of the witnesses, the very introduction of the prejudicial evidence made it more likely that the jury ultimately believed Greeley instead of Crotts.

To reiterate: Jurors were told that Crotts was on parole for an undisclosed felony; jurors then heard testimony that Crotts had told Greeley that he was wanted for killing a police officer. These two pieces of evidence most likely led jurors to make the obvious, but mistaken inference that Crotts had been convicted of killing a police officer. Courts have recognized that such false and prejudicial innuendos induce the jury to convict. In Bradley , we noted that evidence of an uncharged murder posed a “tremendous risk ... that the jury decided that [the defendants] should not go unpunished because of their propensity for violence.” 5 F.3d at 1321-22 .

Finally, the presentation of the prejudicial evidence at the end of the trial and the absence of a limiting instruction (due to Crotts’s counsel’s failure to object to the evidence) only magnified the prejudicial effect. See United States v. Jenkins, 7 F.3d 803, 808 (9th Cir.1993) (prejudicial evidence was not harmless because, in part, it was presented at end of trial and therefore “freshest in the mind of the jury when they retired to deliberate”).

IV. CONCLUSION

For the foregoing reasons, we affirm the district court’s grant of Crotts’s petition for a writ of habeas corpus and remand for further proceedings.

AFFIRMED.

. Greeley, the passenger in Crotts’s truck, testified that after Crotts jumped into the truck, Sehoonmaker hit him with a flashlight; Crotts then reached for the keys and started the truck; the truck veered right, then left; Greeley heard gunshots, and then felt the track stop. . The undisclosed felony of which Crotts was convicted in Oregon was sodomy and sexual abuse. . In light of the Court's recent decision in Duncan v. Henry, we see no need to apply the exhaustion analysis set forth in Tamapua v. Shimoda, 796 F.2d 261 (9th Cir.1986) and Miller v. Rowland, 999 F.2d 389 (9th Cir.1993). . In defining the required showing under the first prong of the Strickland analysis, the Supreme Cotut cautioned that a counsel's conduct does not constitute ineffectiveness if it may be construed as the result of a "tactical decision.” 466 U.S. at 689 , 104 S.Ct. at 2065 .