Ohio Rev. Code § 749.31
Except where the contract is for equipment, services, materials, or supplies available from a qualified nonprofit agency pursuant to sections 4115.31 to 4115.35 of the Revised Code, the board of hospital trustees shall enter into a contract for work or supplies where the estimated cost exceeds fifty thousand dollars with the lowest and best bidder. Where the contract is for other than the construction, demolition, alteration, repair, or reconstruction of an improvement, the board shall enter into the contract when the bidder gives bond to the board, with such security as the board approves, that the bidder will perform the work and furnish materials or supplies in accordance with the contract. On the failure of such bidder within a reasonable time, to be fixed by the board, to enter into bond with such security, a contract may be made with the next lowest and best bidder, and so on until a contract is effected by a contractor giving such bond. The board may reject any bid.
R.C. § 749.31