Ohio Rev. Code § 323.132
If one-half of the current taxes charged against an entry of real estate is not paid on or before the thirty-first day of December of the year for which they are charged or on or before the last day for such payment as extended pursuant to section 323.17 of the Revised Code, that amount, together with the penalty charged under division (A)(1) of section 323.121 of the Revised Code and all delinquent taxes or installment thereof charged against such entry may be paid at any time prior to the date on which tax bills for the second half collection are mailed and delivered, without at the same time requiring payment of the second half of such taxes.
If the total amount of such current taxes, delinquent taxes, and all installment payments due under section 323.31 of the Revised Code are not paid on or before the twentieth day of June, next thereafter, or on or before the last day for that payment as extended pursuant to section 323.17 of the Revised Code, the balance of the amount of such taxes, plus all penalties and interest imposed by section 323.121 of the Revised Code, constitutes the delinquent taxes on such entry, which shall be placed on the delinquent land list and duplicate pursuant to section 5721.011 of the Revised Code and shall be collected in the manner prescribed by law, unless the property against which such taxes are charged is the subject of an application for exemption from taxation pursuant to section 5715.27 of the Revised Code.
A taxpayer may tender, and the treasurer shall accept, the full amount of delinquent taxes charged against an entry of real estate without having to tender at the same time the payment of any current taxes that are due and payable.
A county treasurer may accept partial payments of taxes. Any overpayment shall be refunded by the treasurer in the manner most convenient to the treasurer. When the amount tendered and accepted is less than the amount due, the unpaid balance shall be treated as other unpaid taxes, and, except when the unpaid amount is the penalty or interest and charges on the unpaid taxes, the treasurer shall notify the taxpayer of such deficiency.
If the taxpayer files with the payment of taxes a copy of an application to the tax commissioner for remission of penalty, or the payment is received within ten days after the last day the taxes may be paid without penalty, the county treasurer shall accept a partial payment in which the only unpaid amount is the penalty for late payment.
If, at any time, and having been provided such documentation as may be found acceptable by the county treasurer, the county treasurer determines that due to a clerical error, a taxpayer has overpaid either the first one-half or second one-half payment of current taxes as charged on the tax list and duplicate, the treasurer may refund the amount of the overpayment to the taxpayer in the manner most convenient to the treasurer.
R.C. §323.132