Ohio Revised Code General Provisions § 1.62

(A) References to particular county officers, boards, commissions, and authorities mean, in the case of a county that has adopted a charter under Article X, Ohio Constitution, the officer, board, commission, or authority of that county designated by or pursuant to the charter to exercise the same powers or perform the same acts, duties, or functions that are to be exercised or performed under the applicable section of the Revised Code by officers, boards, commissions, or authorities of counties that have not adopted a charter.  If any section of the Revised Code requires county representation on a board, commission, or authority by more than one county officer, and the charter vests the powers, duties, or functions of each county officer representing the county on the board, commission, or authority in fewer officers or in only a single county officer, the county officers or officer shall succeed to the representation of only one of the county officers on the board, commission, or authority.  If any vacancy in the representation of the county on the board, commission, or authority remains, the taxing authority of the county shall adopt a resolution to fill the vacancy.

(B) References to resolutions mean, in the case of a county that has adopted a charter under Article X, Ohio Constitution, the appropriate form of legislation permitted by or pursuant to the charter.