Ohio Rev. Code § 7.11
A proclamation for an election, an order fixing the time of holding court, notice of the rates of taxation, bridge and pike notices, notice to contractors, and such other advertisements of general interest to the taxpayers as the county auditor, county treasurer, probate judge, or board of county commissioners deems proper shall be published in a newspaper of general circulation, as defined in section 7.12 of the Revised Code at the county seat. In counties having cities of eight thousand inhabitants or more, not the county seat of such counties, additional publication of such notice shall be made in a newspaper of general circulation, as defined in such section, in such city.
The cost of any publication authorized by this section, which shall be printed in display form, shall be the government rate established by such newspaper under section 7.10 of the Revised Code.
R.C. § 7.11