The treasurer of the board of trustees, or board of directors, or board of management of any institution receiving state aid shall furnish to the auditor general, to be placed on file in his office, on or before the fifteenth day of each month, a sworn statement of the items of receipts and payments on account of such institutions for the preceding month, and shall, if required by the governor, the auditor general or the state treasurer, exhibit the original vouchers, or bills of items, for such payments.