The city auditor shall keep in the city auditor’s office a curbing repair assessment book and shall enter therein curbing costs certified by the street commissioner as an assessment against the lots or parcels of land fronting on or adjoining such curbing, and the name of the owner of such lots or parcels of land if known to the city auditor. At a regular meeting, the governing body shall review all assessments and hear all complaints against the same and approve the same as finally adjusted. The city auditor shall deliver to the county auditor a duplicate of all assessment rolls containing assessments made under the provisions of this chapter, and the county auditor shall extend the assessments in the proper column against the property assessed. Each assessment shall be collected and the payment thereof enforced as county and state taxes are collected and enforced. When collected, the assessment shall be paid over by the county treasurer to the city auditor in the same manner as other taxes.