(a) The cost of the construction of sidewalks, curbs and gutters shall be paid by assessment of a special and local tax on the property abutting thereon, in the manner provided by law; and the urban county government shall not be liable for any part of such cost. The contractor may, by suit in his own name or in the name of the urban county government, enforce collection of such local and special tax and foreclose the lien therefor; but all such suits shall be at the sole cost and expense, both ordinary and extraordinary, of the contractor, and the urban county government shall not be liable therefor.
(b) All special assessments and taxes for the construction of sidewalks, curbs and gutters shall be due and payable at the office of the director, division of revenue immediately upon the publication of the ordinance assessing such taxes. The commissioner of finance shall keep a record of all such special taxes and assessments in his office in a book to be provided for that purpose, and upon the payment of any tax to the director, division of revenue he will report the same to the commissioner of finance, who will make proper entry thereof on such record, whereupon the lien created by such tax shall stand released.