Ohio Rev. Code Ann. § 307.29

The board of county commissioners may, by agreement with the city council, the director of public safety or his successor, or the person or board charged with the erection, maintenance, or repair of police stations, jails, police and municipal courthouse and courtrooms, lease to any municipal corporation in the county suitable quarters in county buildings, erected or to be erected, for municipal courts, police stations, prosecutors' offices, probationers' offices, and other similar municipal purposes. Whenever the board of any county has made such an agreement with a municipal corporation the board may erect a county building anticipating and making provision for such municipal quarters.