Section 75.54 shall be construed to permit the reassessment, by or under the direction or authority of any city, of the property, real and personal, therein, which city, before and until the passage of these statutes, was authorized by law to make its own tax sales, tax certificates and tax deeds by its own proper officers. And in and for and in respect to every such city and the property, real and personal, therein the mayor and council thereof, the assessors thereof, the city clerk thereof, the board of equalization thereof, and the city treasurer thereof shall, as to any such city and the wards therein, respectively exercise all the powers and perform all the duties and proceed in the manner hereinbefore provided in respect to towns, villages and other cities, and exercise the powers and perform the duties devolved upon the board of supervisors, upon the assessors, upon the town clerk, upon the board of review and upon the town treasurer, respectively, for the reassessment of taxes and the collection thereof.