Ohio Rev. Code § 3709.281
A board of health of a city or general health district may enter into an agreement with the legislative authority of a municipality in which such health district is totally or partially located, and such legislative authority may enter into an agreement with such board of health, whereby such board of health undertakes, and is authorized by such legislative authority to exercise any power, perform any function, or render any service, in behalf of such legislative authority which such legislative authority may exercise, perform, or render.
Upon the execution of such agreement and within the limitations prescribed by it, such board of health may exercise the same powers as such legislative authority possesses with respect to the performance of any function or the rendering of any service, which, by such agreement, it undertakes to perform or render, and all powers necessary or incidental thereto, as amply as such powers are possessed and exercised by such legislative authority directly. Any agreement authorized by this section does not suspend the possession by such legislative authority of any power or function exercised or performed by such board of health in pursuance of such agreement, and no board of health, by virtue of any agreement entered into under this section, shall acquire any power to levy taxes in behalf of such legislative authority unless approved by a majority of the electors of the municipality.
Every agreement entered into under this section shall provide, either in specific terms or by prescribing a method for determining the amounts, for any payments which are to be made by the legislative authority in consideration of the performance of the agreement. Such payments shall be made to the health fund of the health district.
R.C. §3709.281