Ohio Rev. Code Ann. § 3501.37

After each election, the precinct election officials of each precinct, except when the board of elections assumes the duty, shall see that the movable booths and other equipment are returned for safekeeping to the fiscal officer of the township or to the clerk or auditor of the municipal corporation in which the precinct is situated. The fiscal officer, clerk, or auditor shall have booths and equipment on hand and in place at the polling places in each precinct before the time for opening the polls on election days, and for this service the board may allow the necessary expenses incurred. In cities, this duty shall devolve on the board.