The part of the refund representing amounts paid to the state, including interest as provided in RCW 84.69.100, shall be paid from the county general fund and the department of revenue shall, upon the next succeeding settlement with the county, certify this amount refunded to the county: PROVIDED, That when a refund of tax funds pursuant to state levies is required, the department of revenue shall authorize adjustment procedures whereby counties may deduct from property tax remittances to the state the amount required to cover the state's portion of the refunds.