Municipalities are authorized to enter into two kinds of contracts for the operation of municipal schools:

• A city school board and a county school board may enter into a contract for the county superintendent of education to supervise the operation of city schools. Such a contract does not alter the distribution of county and state funds to city schools, but the city is authorized to devote its school funds to payment of the proportionate cost of the maintenance of such schools. The indebtedness of the city school system remains the obligation of the city. T.C.A. § 49-2-1001.
• The boards of education of two or more school systems are authorized to enter into a contract to establish, maintain and operate a public school or schools jointly. If the city does not have a school board, the city’s governing body may enter into the contract. T.C.A. §§ 49-2-1101, et seq.