According to this Fresno Bee story, some California county election officials have been thinking about charging political parties for the cost of administering elections for party office. But they have given up on the idea. The story says if the counties did charge the parties, the costs for electing county central committee members in Fresno County alone would be between $200,000 and $300,000 each.
About half the states have government-administered elections to enable parties to choose party officers, and the other half of the states don’t. In those states, party officers are all chosen in party meetings. California permits parties to opt out of public elections for party office, and the Libertarian Party has opted out. Thanks to John Tuteur for the link.