Ohio Rev. Code Ann. § 971.071

Notwithstanding any other provision in this chapter, an owner of land as defined in division (D)(2) of section 971.01 of the Revised Code is responsible for fifty per cent of the total cost of building and maintaining in good repair a partition fence between that owner and the owner of adjoining property unless a written agreement has been entered into under section 971.04 of the Revised Code.