Ohio Rev. Code Ann. § 5579.03

If a road is established as a part of the line or boundary of a township or municipal corporation, the board of township trustees of such adjoining townships and legislative authority of such municipal corporation, shall meet at a convenient place as soon after the first Monday of March as convenient, and apportion such road between the townships, or township and municipal corporation, as justice and equity require. The boards of the respective townships and legislative authority of the municipal corporation shall cause the road to be opened and improved accordingly, and shall thereafter cause their respective portions to be worked and kept in proper repair.