Fitness and character of parents and others contending for custody of child or other person is often in dispute in custody contests and evidence of the character traits and propensities of the contending parties is not barred by the rule prohibiting the use of a person's character to show the person's conduct.

See United States v. Gricco, 277 F.3d 339, 352-353 (3d Cir. 2002) (upholding trial court's exclusion into evidence of defendants' state acquittals because (1) "a judgment of acquittal is not usually admissible to rebut....There is a hearsay exception for evidence of a final judgment, entered after a trial or upon a plea of guilty (but not upon a plea of nolo contendere), adjudging a person guilty of a crime punishable by death or imprisonment in excess of one year, to prove any fact essential to sustain the judgment, but not including, when offered by the Government in a criminal prosecution for purposes other than impeachment, judgments against persons other than the accused.

Fed. R. Evid. 413(d) ("For purposes of this rule and Rule 415, "offense of sexual assault" means a crime under Federal law or the law of a State (as defined in section 513 of title 18, United States Code) that involved-- (1) any conduct proscribed by chapter 109A of title 18, United States Code; (2) contact, without consent, between any...Federal Rule of Evidence 413(d) provides that for purposes of Rule 413 and also for purposes of Federal Rule of Evidence 415 an "offense of sexual assault" is a crime under Federal law or the law of a State (as defined in section 513 of title 18, United States Code) that involved-- (1) any conduct proscribed by chapter 109A of title 18, United States Code; (2) contact, without consent, between any part of the defendant's body or an object and the genitals or anus of another person; (3) contact, without consent, between the genitals or anus of the defendant and any part of another person's body; (4) deriving sexual pleasure or gratification from the infliction of death, bodily injury, or physical pain on another person; or (5) an attempt or conspiracy to engage in conduct described in paragraphs (1)-(4).

Combs v. Wilkinson, 315 F.3d 548, 554-556 (6th Cir. 2002) (holding, in plaintiff death row inmates' civil rights action against defedant corrections supervisors and officers for use of excessive force, that the trial....An exception to the hearsay rule applies to the following records of government offices and agencies: (A) public records that set forth the activities of the government office or agency; (B) public records that set forth observations that a government office or agency was required to make and report but this exception does not apply in criminal cases to observations of police officers and other law enforcement personnel; or (C) in civil actions and proceedings and in criminal cases when offered against the government, factual findings resulting from an investigation made pursuant to authority granted by law, unless the sources of information or other circumstances indicate the untrustworthiness of such findings.