Ohio Rev. Code Ann. § 3375.31

The board of library trustees of a regional library district may annually, during the month of May, certify to the boards of county commissioners of counties in such district the amount of revenue anticipated from all sources other than a tax levy on the taxable property of such district. The boards of county commissioners may annually levy a tax on the taxable property of such district situated within their respective counties, not to exceed one mill, for the purpose of providing funds for library operation pursuant to said certification.