Ohio Rev. Code § 1711.31
When the title to grounds and improvements occupied by an agricultural society is in the board of county commissioners, the control and management of such lands and improvements shall be vested in the board of directors of such society so long as they are occupied by it and used by it for holding agricultural fairs.
When the title to such grounds or improvements, or any part thereof, is appropriated for another public purpose or sold to an agency which has the power to so appropriate, if such society notifies the county commissioners of an intention to proceed under section 1711.25 to 1711.32, inclusive, of the Revised Code, to replace such property, the moneys shall be divided between the county and the society in accordance with the respective values of the interest of each in such property, as determined by agreement of the parties or pursuant to section 163.18 of the Revised Code. Each share of such moneys shall be held by the respective party solely for use in replacement of its respective interest in such property notwithstanding any limitations on expenditures otherwise provided in Chapter 1711. of the Revised Code.
Moneys realized by the society in holding county fairs and from renting or leasing all or part of the grounds and buildings for the conduct of fairs or otherwise, over and above the necessary expenses thereof, shall be paid into the treasury of the society and used as a fund for keeping such grounds and buildings in good order and repair and for making other improvements deemed necessary by the society's directors.
R.C. § 1711.31