Where the duties of assessing property and collecting city taxes are performed for the city by the county assessor and the county tax collector, in the manner provided by law, a certified copy of the diagram and assessment shall be filed with the county auditor on or before the tenth day of August. In each such diagram and assessment so filed with the county auditor, the descriptions of the properties reported shall be the descriptions used for the same properties on the map books of the county assessor for the then current year. The county auditor shall enter the amounts of the respective assessments on the county tax roll opposite the respective parcels of land and thereafter the amounts shall be collected at the same time and in the same manner as county taxes are collected and all laws applicable to the levy, collection and enforcement of county taxes shall be and are hereby made applicable to such special assessment taxes.