An authority created pursuant to this article shall be eligible to receive state reimbursement for jail construction and operation in accordance with the provisions of Article 3 (§ 53.1-80 et seq.) of this chapter. State reimbursement for the cost of the project shall be made to the authority and shall be determined as if each participating political subdivision in the authority had contributed its pro rata share of such cost. However, when an authority created pursuant to this article enters into an agreement with one or more political subdivisions not participating in the authority for the purpose of construction and operating a jail, that share of the state reimbursement due to any political subdivision not participating in the authority shall be made directly to such political subdivision in accordance with the provisions of Article 3 of this chapter. The Commonwealth shall fund the positions of superintendent, correctional officers, and two-thirds of the salaries of required medical or treatment personnel on a basis approved by the State Compensation Board. Such salaries shall be paid in the manner provided in § 15.2-1609.2, and such section shall be applicable mutatis mutandis to such superintendent. The superintendent of the correctional facility shall report on the first day of each month to the Director of the State Department of Corrections to give the record of each prisoner received during the preceding month on blank forms to be furnished by the Director, to state whether the offense for each prisoner is for violation of state law or of city or town ordinance. The report shall be signed by both the superintendent and chairman of the authority. Either signer found guilty of willfully falsifying the information contained in such report shall be guilty of a Class 1 misdemeanor. If any superintendent fails to send such report within five days after the date when the report is to be forwarded, the Director shall notify the superintendent of such failure. If the superintendent fails to make the report within ten days from that date, then the Director shall cause the report to be prepared from the books of the superintendent and shall certify the cost thereof to the Comptroller. The Comptroller shall issue his warrant on the Treasurer for that amount, deducting the same from any funds that may be due the superintendent by the Commonwealth.