Ohio Rev. Code § 3127.42: Award of fees, expenses and costs to prevailing party.

(A) A court shall award the prevailing party in an action to enforce a child custody determination, including a state, necessary and reasonable expenses incurred by or on behalf of the party, including costs, communication expenses, attorney's fees, investigative fees, expenses for witnesses, travel expenses, and child care during the course of the proceedings, unless the party from whom fees or expenses are sought establishes that the award would be clearly inappropriate.

(B) The court shall not assess fees, costs, or expenses against a state or a political subdivision of a state unless authorized by law other than this chapter.