Ohio Rev. Code § 5705.22
The board of county commissioners of any county, at any time and in any year, after providing the normal and customary percentages of the total general fund appropriations for the support of county hospitals, by vote of two-thirds of all members of said board, may declare by resolution that the amount of taxes which may be raised within the ten-mill limitation will be insufficient to provide an adequate amount for the support of county hospitals, and that it is necessary to levy a tax in excess of the ten-mill limitation to supplement such general fund appropriations for such purpose, but the total levy for this purpose shall not exceed sixty-five one hundredths of a mill.
Such resolution shall conform to the requirements of section 5705.19 of the Revised Code, and shall be certified to the board of elections not less than ninety days before the general election and submitted in the manner provided in section 5705.25 of the Revised Code.
If the majority of electors voting on a levy to supplement the general fund appropriations for the support of county hospitals vote in favor of the levy, the board of said county may levy a tax within such county at the additional rate in excess of the ten-mill limitation during the period for the purpose stated in the resolution or at any less rate or for any of the said years.
R.C. § 5705.22