Ohio Rev. Code § 3.12
An officer or agent of the state or of any county, township, or municipal corporation who is charged or entrusted with the construction, improvement, or keeping in repair of a building or work of any kind, or with the management of or providing for a public institution, shall make no contract binding or purporting to bind the state, or such county, township, or municipal corporation, to pay any sum of money not previously appropriated for the purpose for which such contract is made, and remaining unexpended and applicable thereto, unless such officer or agent has been authorized to make such contract. If such officer or agent makes or participates in making a contract without such appropriation or authority, he is personally liable thereon, and the state, county, township, or municipal corporation in whose name or behalf the contract was made shall not be liable thereon.
R.C. §3.12