Representative Michele Bachmann’s presidential hopes ended 20 months ago, but her brief and chaotic campaign continues to be the focus of ethics investigations.

The latest is a federal inquiry into whether an outside “super PAC” improperly coordinated strategy with Mrs. Bachmann’s campaign staff, including her husband, in violation of election laws.

The Department of Justice demanded records from the super PAC last week of its finances and its communications with Mrs. Bachmann; Marcus Bachmann, her husband; and former staff members, according to a grand jury subpoena reviewed by The New York Times.

The investigation appears to stem from a complaint a former campaign staff member made to the Federal Election Commission and to the F.B.I. The staff member told of overhearing the president of the super PAC asking a Bachmann senior adviser about buying advertising on radio and TV stations in Des Moines ahead of the Iowa caucus on Jan. 3, 2012.