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.

Coordination between a campaign and a super PAC violates federal election law if it meets certain criteria, said Paul S. Ryan, a senior counsel at the independent Campaign Legal Center.

Mrs. Bachmann is already the subject of a House Ethics Committee investigation into her campaign finances and allegations her staff was improperly used to promote her political biography, “Core of Conviction.”

Mrs. Bachmann, 57, who announced in May that she would not seek a fifth term from her Minnesota district next year, said at the time that her decision was unrelated to the ethics charges.

Briefly the front-runner in the Republican primary, she won a much-watched Iowa straw poll in August 2011, appearing on the cover of Newsweek, but she finished last in the caucus four months later and quit the race.

The turmoil of her final weeks has spawned multiple accusations of impropriety. A coordinator for Christian home-school families sued Mrs. Bachmann, accusing her of stealing a mailing list; the suit was recently settled. An Iowa state senator who was chairman of Mrs. Bachmann’s campaign is under investigation by the Iowa Supreme Court over whether he was improperly paid.

In a complaint to the F.E.C. in February, Peter Waldron, a Florida Republican operative hired to enlist evangelical Iowa pastors, described overhearing the president of the super PAC ask Brett O’Donnell, a senior campaign adviser, about radio and TV stations.

In an interview on Thursday, Mr. Waldron said Mr. O’Donnell had replied, “I’ll call you tomorrow.”

Election law prohibits substantial coordination, though not all contacts, between campaigns and super PACS, Mr. Ryan said.

Mr. Waldron, who calls himself a whistle-blower, also disclosed an e-mail from Mr. Bachmann describing a phone call Mr. Bachmann made to a donor asking for $7,000. In the e-mail, Mr. Bachmann wrote that the donor had agreed to give the money through the super PAC. He concluded: “Praise the Lord!! Thank you Peter for your servant leadership.”

Mr. Ryan said the call appeared to violate a rule against campaign staff members raising more than $5,000 for a super PAC. A lawyer for Mrs. Bachmann did not respond to a request for comment.

The super PAC, the National Fiscal Conservative PAC, reported the $7,000 donation from the donor, August A. Busch III, in December 2011, according to the Center for Responsive Politics.

Bill Hemrick, the president of the super PAC, said in an interview that he had advised Mr. Bachmann to call Mr. Busch to ask for the donation. He did so, he said, after Mr. Waldron called him first to ask for the money for use by the campaign.

Mr. Waldron, who has a controversial past, has been dismissed by other former Bachmann staff members as a disgruntled employee who had limited responsibilities. Last month he published a critical e-book, “Bachmannistan: Behind the Lines.”

In 2006 he was jailed briefly in Uganda for possession of assault rifles, according to news reports. In the 1990s he led a Florida youth charity that received more than $600,000 in state and local grants before it collapsed amid questions about its effectiveness, according to The St. Petersburg Times, now The Tampa Bay Times.