
514 F.3d 729 (2008)
Albert J. PRICE, Petitioner-Appellant,
v.
Michael THURMER, Respondent-Appellee.
No. 06-4116.
United States Court of Appeals, Seventh Circuit.
Argued November 7, 2007.
Decided February 1, 2008.
*730 Jerold S. Solovy, John K. Min (argued), Jenner & Block, Chicago, IL, for Petitioner-Appellant.
Aaron R. O'Neil (argued), Office of the Attorney General Wisconsin Department of Justice, Madison, WI, for Respondent-Appellee.
Before POSNER, WOOD, and WILLIAMS, Circuit Judges.
POSNER, Circuit Judge.
Back in 1991 Albert Price was driving his truck and struck a pedestrian and then slammed into the back of another vehicle, causing a four car pile-up. He leapt out of his truck swinging a machete and injured three passersby before he was disarmed. He was convicted by a jury in a Wisconsin state court of attempted murder and other crimes, and was sentenced to 185 years in prison. The jury rejected his plea of not guilty by reason of insanity, primarily it seems on the basis of testimony by Dr. Vincent Giannattasio, a psychiatrist called as a witness by the state. Two other psychiatrists testified: Dr. Walter McDonald, Price's expert, testified that Price was indeed insane; Dr. Robert Drom, a court-appointed expert, was unable to form an opinion about Price's mental condition. The prosecution did not tell Price's lawyer (and apparently did not know) that the federal government had indicted Giannattasio for Medicare fraud. The indictment had been dismissed, but the government's appeal from the dismissal was pending during Price's trial. The dismissal was reversed after the trial, United States v. Giannattasio, 979 F.2d 98 (7th Cir.1992), but the government later dismissed criminal charges against Giannattasio, instead successfully suing him in a civil case for fraud.
Price appealed his conviction to the Wisconsin court of appeals, arguing that the failure of the prosecution to disclose the indictment was a Brady violation. The court disagreed. State v. Price, 2002 WL 563375, at *2 (Wis.App. Apr. 17, 2002) (per curiam). It ruled that since under Wisconsin's law of evidence an indictment cannot be used to impeach a witness's credibility, State v. Reynolds, 28 Wis.2d 350, 137 N.W.2d 14, 20 (1965); see also State v. Cathey, 32 Wis.2d 79, 145 N.W.2d 100, 105 (1966); State v. Raether, 259 Wis. 391, 48 N.W.2d 483, 485 (1951); compare Wis. Stat. § 906.09(1), the information about Giannattasio's indictment was immaterial. There is no obligation to turn over immaterial evidence to a defendant, United States v. Rodriguez-Rivera, 473 F.3d 21, 26 (1st Cir.2007); United States v. Jones, 399 F.3d 640, 648 (6th Cir.2005), unless it is apparent that it might lead to the discovery of material evidence. United States v. Perez, 280 F.3d 318, 349 (3d Cir.2002); Bradley v. Nagle, 212 F.3d 559, 567 (11th Cir.2000); East v. Johnson, 123 F.3d 235, 238 (5th Cir.1997). In the alternative, the court held that any Brady error was harmless, because the Medicare fraud was unrelated to Giannattasio's testimony about Price's sanity and therefore could not have affected the jury's decision.
Before appealing his conviction, Price had initiated a state postconviction proceeding complaining about the effectiveness of his trial lawyer. After conducting *731 an evidentiary hearing, the trial judge rejected the complaint, as did the Wisconsin court of appeals on Price's appeal from his conviction. Having exhausted his state remedies, Price petitioned for federal habeas corpus; he was denied relief, without a hearing.
He contends that his right to confront Dr. Giannattasio was infringed because he could not tell the jury (not having been informed by the prosecution) that Giannattasio had been indicted for fraud. A jury might rationally discount the testimony of a witness who had committed a crime involving fraud. Fed.R.Evid. 609(a)(2); United States v. Chevalier, 1 F.3d 581, 583-84 (7th Cir.1993); United States v. Mejia-Alarcon, 995 F.2d 982, 988-89 (10th Cir.1993); see also State v. Gary M.B., 270 Wis.2d 62, 676 N.W.2d 475, 483 (2004). But no more than Wisconsin evidence law do the Federal Rules of Evidence permit impeachment by an indictment, as distinct from a conviction, Fed. R.Evid. 609; Michelson v. United States, 335 U.S. 469, 482, 69 S.Ct. 213, 93 L.Ed. 168 (1948); United States v. Chance, 306 F.3d 356, 385 (6th Cir.2002); Dowthitt v. Johnson, 230 F.3d 733, 756 (5th Cir.2000), and we cannot believe that this limitation infringes the right of confrontation.
Of course, under federal as under Wisconsin law, "specific instances of the conduct of a witness, . . . in the discretion of the court, if probative of truthfulness or untruthfulness, can be inquired into on cross-examination" concerning the witness's "character for truthfulness or untruthfulness," Fed.R.Evid. 608(b); see Wis. Stat. § 906.08(2); see also Lindh v. Murphy, 124 F.3d 899, 901 (7th Cir.1997); United States v. Machado, 804 F.2d 1537, 1545 (11th Cir.1986); United States v. Collins, 472 F.2d 1017, 1019 (5th Cir.1972), though it cannot be proved by extrinsic evidence. United States v. Dabney, 498 F.3d 455, 459 (7th Cir.2007); United States v. Thomas, 467 F.3d 49, 56 (1st Cir.2006); Wis. Stat. § 906.08(2); State v. Sonnenberg, 117 Wis.2d 159, 344 N.W.2d 95, 102-03 (1984). So the trial court could have allowed Price's lawyer to ask Giannattasio whether he had committed Medicare fraud (had the lawyer known about the prosecution), though if as is quite probable Price had answered "no" the lawyer could not have presented evidence to prove the fraud and the effort at impeachment would have fizzled.
This suggests a basis for a finding of harmless error, but one different from that of the Wisconsin court of appeals. Evidence need not, as that court thought, be "relevant" to any issue to be usable to impeach a witness; all it need do is undermine his credibility, as is obvious when a witness's criminal record is used to impeach his credibility under Fed.R.Evid. 609 in a case in which he is not a party. Harmlessness aside, Price did not argue in the Wisconsin court of appeals that he should have been told about the indictment so that he could impeach Giannattasio not with the indictment but with the alleged Medicare fraud that had given rise to it. He argues the point in this court, by a different lawyer, but it is too late. See 28 U.S.C. § 2254(b)(1); O'Sullivan v. Boerckel, 526 U.S. 838, 844-45, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999); Simpson v. Battaglia, 458 F.3d 585, 593 (7th Cir.2006).
Price had suggested another way in which he could have used the pending federal charges to impeach Dr. Giannattasio: by showing that Giannattasio had a motive to testify favorably to the state in Price's case because if he did so the state prosecutors might put in a good word for him with their federal counterparts. That's quite a stretch, but in any event the argument has been abandoned in this court. And since it seems that no one on *732 the prosecution team knew about Giannattasio's indictment; and it was a matter of public record readily accessible to Price's lawyer, unlike the circumstances of Boss v. Pierce, 263 F.3d 734, 744 (7th Cir.2001); United States v. Payne, 63 F.3d 1200, 1208-09 (2d Cir.1995), and United States v. Perdomo, 929 F.2d 967, 973 (3d Cir.1991), the prosecution had no obligation to disclose it to the defense. United States v. Tadros, 310 F.3d 999, 1005 (7th Cir.2002); United States v. Young, 20 F.3d 758, 764 (7th Cir.1994); Matthews v. Ishee, 486 F.3d 883, 890-91 (6th Cir.2007); United States v. Infante, 404 F.3d 376, 386-87 (5th Cir.2005); United States v. Delgado, 350 F.3d 520, 527 (6th Cir.2003).
As for ineffective assistance of counsel, Price complains not about his trial lawyer's failing to discover the indictment of Giannattasio but about the lawyer's waiving a hearing on Price's mental competence to stand trial and withholding essential information from the court-appointed expert who testified about Price's mental state when he committed the crimesDr. Drom, the expert who could not make up his mind about Price's sanity. Thus there are two issues relating to the lawyer's handling of the issue of Price's sanity: whether Price was mentally competent to stand trial and whether he had been insane when he committed the crimes for which he was being tried.
Price had a long history of mental disease, and had been diagnosed as a paranoid schizophrenic; and his original lawyer had succeeded in getting the judge to agree to conduct a competency hearing. Wis. Stat. § 971.14(4)(b). But his new lawyer (the one about whom he is complaining), who had been appointed just minutes before the hearing was scheduled to begin, asked for a 24-hour adjournment and when it was up told the judge that Price was waiving the hearing. The Wisconsin court of appeals first said that the lawyer had made this decision, State v. Price, supra, at *1, but later said that it had been made jointly by the lawyer and Price, id. at *8which raises the question whether the judge should have accepted the waiver without first determining Price's competence. The lawyer did not recall having discussed competence with Price, but he thought that probably he had and that in any event "there wasn't any doubt in my mind that Mr. Price was competent, and he felt the same way." Dr. Robert Miller, whom the court had asked to report on Price's competence to stand trial, had reported that he was competent, but Price's lawyer had failed to give him all the documents that the lawyer possessed concerning Price's mental history.
Concerning Price's mental condition when he committed the crimes, his lawyer had amassed a number of reports concerning the traffic accident and the melee that had ensued, as well as medical records (including the ones he had not shown Dr. Miller at the time of the inquiry into Price's competency to stand trial). He gave some of this material to the court-appointed expert witness at trial, Dr. Drom, but not all. He especially neglected to give Drom the reports of persons who had observed Price in the days preceding the machete attack and medical reports of Price's previous bouts of mental illness. He did give Drom an oral summary of the witness reports, but Drom was unwilling to offer an opinion on Price's mental condition on the basis of those summaries.
At the state postconviction hearing, a new expert retained by Price, Dr. John Marshall, examined the full record and concluded that it was "not, in my opinion, even a close call" that "Mr. Price suffered from a mental disease at the time of the offense, and that the disease caused him to *733 not know right from wrong and to be unable to conform his behavior to the requirements of the law." He opined that experts who had not had access to reports of the "observations of people close to [Price] just prior to this incident" would have been "severely handicapped" in rendering an opinion on Price's mental condition during the attack.
Drom did not testify or provide an affidavit in the postconviction proceeding, so we do not know whether his opinion (or rather lack of opinion) concerning. Price's sanity would have been altered had he seen the additional reports. Apparently it was not Price's fault that Drom did not participate in the postconviction proceeding. Drom had retired and refused to testify. The state does not argue that Price could or should have compelled him to do so.
The Wisconsin court of appeals gave short shrift to the ineffective-assistance issues, stating that "Price had not demonstrated any signs or symptoms of any significant mental disorder during his stay while being evaluated for competence. Also, trial counsel informed Dr. Drom of the pertinent eyewitness accounts of Price's behavior during the weekend before the crimes. Drom indicated at trial that those accounts did not change his inability to form an opinion since he could not determine the credibility of the behavioral observations. Giving Dr. Drom the actual reports would not have changed his testimony because he still could not assess the credibility of the reported observations. Finally, the claim that trial counsel should have presented evidence found in the police reports during the NGI [not guilty by reason of insanity] phase [of the trial,] ignores the fact that during the first portion of the trial, the jury heard descriptions of Price's conduct, statements and behavior. Price's own expert [Dr. McDonald] explained how the observations of various people played a role in his determination that Price was NGI. Repetition of this evidence was not necessary." There is no mention of the attempt by Price's lawyer to make his own competency determination, of Dr. Marshall's testimony, or of whether a lawyer's providing an expert witness with an oral summary of reports of fact witnesses is an adequate substitute for giving the reports to the expert to read for himself.
We cannot be certain that the lawyer's handling of the insanity aspects of the case was prejudicial to Price, as we are well aware that insanity is not a defense to which many jurors are sympathetic; we do not know whether Dr. Drom's testimony would have been altered had he had the additional reports; and it is very difficult to predict the outcome of a competency hearing that was never held. We cannot conclude, therefore, that the Wisconsin courts acted unreasonably in rejecting Price's claims of ineffective assistance of counsel. But there is so much missing from the state appellate court's evaluation of the claims that we cannot determine the reasonableness of that evaluation without asking the district court to take evidence on the matter. When the merits of a petition for habeas corpus cannot be determined from the record compiled in the state court, through no fault of the petitioner (compare 28 U.S.C. § 2254(e)(2)), the district court is authorized, and may be directed by the court of appeals, to conduct its own hearing and make appropriate findings, here on whether Price's defense was prejudiced by the mistakes committed by his lawyer with regard to insanity. E.g., Williams v. Taylor, 529 U.S. 420, 432, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000); Davis v. Lambert, 388 F.3d 1052, 1064-65, 1067 (7th Cir.2004); United States ex rel. Hampton v. Leibach, 347 F.3d 219, 244-45 (7th Cir.2003); Barkell v. *734 Crouse, 468 F.3d 684, 697-99 (10th Cir. 2006); Hendricks v. Vasquez, 974 F.2d 1099, 1109-10 (9th Cir.1992); Lawrence v. Armontrout, 900 F.2d 127, 131 (8th Cir. 1990).
The ruling relating to Dr. Giannattasio is affirmed, but the judgment denying all relief is reversed and the case is remanded to the district court for further proceedings consistent with this opinion.
