Within thirty days after June 30, 1971, and each year thereafter, the department shall certify to the Director of Administrative Services all amounts not previously certified due to each state institution from the several counties having patients chargeable thereto. The Director of Administrative Services shall thereupon notify the county clerk of each county of the amount each county owes. The county board shall add to its next levy an amount sufficient to raise the amount certified as due. The county shall pay the amount certified into the state treasury on or before the next June 1 following such certification.