Ohio Rev. Code § 3501.161
The board may decide by the affirmative vote of at least three members to fill a vacancy in the office of chairman or director with a person belonging to the opposite political party from that to which the outgoing officer belonged. After such a vote, the vacancy shall be filled and all other officers shall be reselected in accordance with the procedures set forth in section 3501.09 of the Revised Code. An officer filling a vacancy and an officer who becomes or remains an officer after the reselection shall serve as an officer for the remainder of the term for which the outgoing officer was selected to serve as an officer. A reselection of officers under this section does not increase or decrease the length of any person's term as member of the board. The director and deputy director shall be of opposite political parties, and the chairman shall be selected from the members of the board of opposite politics from those of the director.
R.C. §3501.161