Davidson said she will pay $6,900 in restitution.
Women make up approximately 51% of the state population, but just under 29% of the state Legislature. Several groups are working to change that.
The special election is the fourth to be scheduled for May 18.
Democrats lost an effort to have the committee hold a public hearing on the legislation, which would amend the Pennsylvania Constitution.
Voters in Westmoreland and Somerset counties will choose between candidates selected by the two major parties.
Republicans blocked a Democratic incumbent from being sworn in because his GOP challenger has disputed the razor-thin results of their election.
Gov. Tom Wolf said the state House Legislative Budget and Finance Committee has no authority to audit the election, and the audit "would be incomplete, duplicative, and unreliable.”