The cost and expenses of any inventory taken under the provisions of this chapter shall be due monthly on the first day of each month as the inventory is being taken, and the state and all other governmental subdivisions and agencies contributing to the payment of the cost and expenses of the same shall be required to pay their pro rata portion of such cost and expenses into the county treasury upon requisition by the presiding officer of the county commission, accompanied by an itemized statement showing the amount due by the particular governmental unit, subdivision, or agency. The Comptroller shall have authority, subject to the approval of the Governor, to draw his warrant on the State Treasurer, payable to the treasurer of any such county, in payment of the state's pro rata of the cost and expenses of any inventory or appraisal.