Ohio Rev. Code § 711.31: Payment of expenses.

When the revision and renumbering of lots are done at the request of a municipal corporation, the expenses shall be paid by such municipal corporation. The board of county commissioners of the county in which unincorporated territory is situated may direct the county auditor and county recorder to make such revision and renumbering and cause the expenses to be paid from the county treasury.

The board may direct such auditor and recorder to make such revision and renumbering of a village, if such board is of the opinion that it is necessary for convenience and efficiency in taxation.