When costs provided in § 4-4-109 have been incurred between departments, the commissioners thereof shall, from time to time, certify to the commissioner of finance and administration the sums due from the one to the other on account of such work, and the commissioner of finance and administration shall thereupon cause to be paid such sums to the creditor department. The payment may be made by check, as other state bills are paid, or by a system of debits and credits, as the commissioner of finance and administration may determine. All sums so received by, or credited to, any department shall be added to the current appropriation made for the support of that department, to the end that its appropriation may not be depleted by reason of the work done for another department.