Introduction of evidence of a witness's prior bad acts for impeachment purposes may be introduced under the discretion of the court. The federal rules of evidence allow questions about prior bad acts of a witness to impeach credibility where, in the court's discretion, they tend to prove or disprove truthfulness. Fed. Rules Evid. 608(b). However, if the witness denies the act, it may not be proved by other evidence unless the act to be proved has some relevance to the case that is independent of its bearing on credibility.
A criminal defendant may introduce opinion evidence or reputation evidence to prove that they did not commit the crime of which they are accused. However, if a criminal defendant does introduce such evidence, the prosecution may then rebut this with evidence of the defendant's bad character.