Jennifer Carnahan was forced out as party chair amid a cloud of allegations.
The lawsuit was filed on behalf of a teenager and her parents.
The GOP donor and strategist is awaiting trial for federal child sex trafficking charges.
The outgoing chairwoman was allowed to break a tie granting her the deal.
"She will never let the truth see the light of day, because in her narcissistic mind, it would ruin her brand," Andy Aplikowski said.
They say any leaders who failed in their legal or moral responsibilities should resign or be fired.
An increasing number of current and former party executives are calling for the embattled chairwoman to step down.
The indictment against Gisela Medina and GOP strategist Anton Lazzaro was unsealed Monday.
The statement revealed that Carnahan had been aware of an allegation of sexual misconduct made against a GOP staffer for months.
The Minnesota Republicans have announced Noem will speak at its March 12 event.
Carnahan was first elected to the position in 2017.
It comes as his supporters have stormed the U.S. Capitol.
Sen. Jerry Relph becomes the fourth senator to contract the disease.
The Senate Majority Leader has attracted plenty of attention for a Thursday tweet.
Republicans have allegedly been encouraging people to run as legal marijuana candidates to take votes away from Democrats.