Upon the levying of any assessment, the city clerk shall transmit the diagram and assessment upon which such levy is based, or a certified copy of said diagram and assessment to the city tax collector or to such other city officer or employee as the city council designates in the resolution levying the assessment or in case the city has adopted a method for collection of taxes by county officers then to the county tax collector, and such county tax collector shall have full power to perform the duties required in this part of the city tax collector.