All warrants for bills on account of state contracts shall be made payable to the order of the person to whom the State is directly indebted, except as provided in § 40-58, and only after an original warrant voucher shall have been presented to the comptroller accompanied by all original bills and any other supporting document as may be required by the comptroller. The original warrant voucher shall have indorsed thereon the approval of the officer in whose department the contracts have been made, and the appropriation to which it is chargeable; and further, each original bill shall be specially certified to by the subordinate officer of the State supervising the work performed, or receiving the materials and supplies as specified in the contracts, that the work has been faithfully performed and that the materials and supplies were in a good and merchantable condition when received, unless the bill is for an advance payment or a deposit to be paid as specified in the department’s contract, in which case the certification of the original bill by the subordinate officer is not required. No warrant shall be issued unless a copy of the contract or bid shall have been filed with the comptroller, together with a statement by the head of the department or agency that made the contract or accepted the bid, naming the appropriation to which the contract or bid is to be chargeable.