Ohio Rev. Code § 5739.34: No preememption.

The levy of any excise, income, or property tax by the state or any political subdivision thereof shall not be construed as preempting the power of a county or transit authority to levy an additional sales tax pursuant to section 5739.021, 5739.023, or 5739.026 of the Revised Code. No tax levied by a board of county commissioners pursuant to section 5739.023 of the Revised Code shall become effective at any time while a tax levied by the board of trustees of a regional transit authority pursuant to such section is in effect in any part of such county.