Refunds ordered by the board of supervisors under this article in respect of county taxes shall be paid by warrant drawn upon the appropriate fund by the county auditor. Refunds ordered in respect of revenue districts, except chartered cities, may be paid by a warrant drawn by the county auditor, upon such available funds, if any, as the revenue district may have on deposit in the county treasury, or in the event such funds are insufficient, then out of funds subsequently accruing to such revenue district and on deposit in the county treasury. Refunds ordered in respect of chartered cities shall be paid in the manner provided for their payment in the charter or ordinances of the
city. Neither any county nor its officers shall refund amounts on behalf of a revenue district from county funds.