Ohio Rev. Code § 5709.10
Market houses and other houses or halls, public squares, or other public grounds of a municipal corporation or township used exclusively for public purposes or erected by taxation for such purposes, land and multi-level parking structures used exclusively for a public purpose and owned and operated by a municipal corporation under section 717.05 of the Revised Code or by an urban township that has adopted a limited home rule form of government under section 504.02 of the Revised Code that charges no fee for the privilege of parking thereon, property used as a county fairgrounds that is owned by the board of county commissioners, property owned by a county agricultural society that is used in furtherance of the purposes of the society, and property of housing authorities created and organized under and for the purposes of sections 3735.27 to 3735.50 of the Revised Code, which property is hereby declared to be public property used exclusively for a public purpose, notwithstanding that parts thereof may be lawfully leased, shall be exempt from taxation.
R.C. § 5709.10