On September 20, Ohio filed this response in the U.S. Supreme Court in Libertarian Party of Ohio v Crites, 21-226. This is the case over the composition of the state Elections Commission, which must contain three members of each of the two largest parties, and one person who is not a member of any party.
The state says that because the Ohio Libertarian Party went off the ballot after the November 2020 election, it has no members and therefore anyone associated with the Libertarian Party is not blocked from applying to be on the commission. It also says that when the case was filed, its member who is a co-plaintiff would not have been eligible anyway, because he was an officer in the Ohio Libertarian Party, and the law does not permit officers of parties to serve on the Commission.