(2) The fund drawn upon for the repairs shall be reimbursed by an assessment of the total cost against the abutting property. After the owner has been given notice and an opportunity to be heard, the county governing body shall by order determine the cost to be assessed against the abutting property. Notice of the determination of the assessment shall be mailed to the owner within 10 days after the cost is determined. The county governing body shall certify the order to the county assessor and shall record the order with the county clerk. The clerk shall indorse on the order the date of filing and record and index it in the special books kept by the clerk for such purpose.