The Registrar of Voters of Napa County, California, believes that qualified political parties that choose to have elections for county central committees should be required to pay the administrative costs of those elections. The California Constitution says that election officials shall conduct such elections for parties that want them. See this story. It is somewhat likely that the Secretary of State will issue an opinion on this controversy, and chances are the Secretary of State will rule that parties don’t need to pay for these elections.
Parties that hold such elections are Democratic, Republican, American Independent, Green, and Peace & Freedom. The Libertarian Party does not use government-administered elections for electing party officials. When Americans Elect was on the ballot, it also did not do so.