Ohio Rev. Code Ann. § 5703.75
This section applies to any tax payable to the state and administered by the tax commissioner. If the total amount of any such tax shown to be due on a return, amended return, or notice does not exceed one dollar, the taxpayer shall not be required to remit the amount due. If the total amount of a taxpayer's overpayment of any such tax does not exceed one dollar, the tax commissioner shall not be required to refund the overpayment.