In the county where the county seat is, within the limits of any city, the county commissioners and the proper corporate authorities of such city shall have the power and they are hereby authorized to agree upon the administration, management, maintenance, control and operation of any or all city hospitals and institutions and of any or all county hospitals and institutions within the county under one board of managers, and to share the expenses thereof in such manner and proportions as shall be agreed upon.
16 P.S. § 5350