Under some circumstances untruthfulness is admissible to impeach a witness.

United States v. Scheffer, 523 U.S. 303, pin? (1998).The exclusion of exculpatory evidence in a criminal trial does not violate the due constitutional right to present a defense if the grounds for exclusion are not arbitrary or disproportionate.

United States v. Cawthorn, 429 F.3d 793, 801-802 (8th Cir. 2005) ("The district court here denied Cawthorn the ability to ask prosecution witnesses questions such as ?Do you lie to authorities??; ?Would you lie to authorities to get something for it??; and ?Do you generally lie?? These questions are...During the cross-examination of a witness -- and during any examination of a witness who is a permissible target for impeachment -- the witness may be asked about specific acts that are indicative of the witness's untruthfulness if such acts are relevant to and probative of the witness' truthfulness or untruthfulness, unless the trial court determines that the acts inquired into are unduly prejudicial.

United States v. LeShore, 543 F.3d 935, 941-942 (7th Cir. 2008) (upholding trial court's admission of the bait money list as a business record because a bank employee testified that "her personal knowledge....Document must have been prepared in the normal course of business.