Ohio Rev. Code Ann. § 703.19

When the census of a city desiring to surrender its corporate rights as such city and be reduced to a village is taken pursuant to the order of the board of county commissioners under section 703.14 of the Revised Code, the necessary expenses thereof shall be paid from the county treasury as other county expenses, but shall be charged against the municipal corporation in which the census was taken, and the amount so paid by the county shall be retained by the county auditor from funds due such municipal corporation at the time of making the next semiannual distribution of taxes.