The Mayor of the District of Columbia may enter into agreements with any of the states, or any political subdivision thereof, where any such institution mentioned in § 10-509.01 is located, for such governmental services as the Mayor shall deem necessary to the efficient and proper government of such institution, and they may, from time to time, agree to modifications in any such agreement; provided, that where the charge for any such service is established by the laws of the state within whose territorial limits such institution is situated, the Mayor may not pay for such service an amount in excess of the charge so established. There is hereby authorized to be appropriated such sums as may be necessary for the making of payment for services under any such agreement.