In all cities in this state not in any county, all the costs and expenses of the assessor of such city or cities, in making the assessments and in the preparation of abstracts of assessment lists and tax bills provided by law, shall be allowed and paid by such city or cities in the same manner as other demands against such city or cities are allowed and paid; and when the aggregate of such costs and expenses for each year shall have been ascertained, the comptroller of such city or cities shall certify same to the director of revenue. After certification by the commissioner of administration, the director of revenue shall certify the claims for payment, and warrant upon the state treasurer shall be issued to the treasurer of such city or cities submitting such certificate for one-half of said sum; provided further, that in all cities in this state not in any county the assessor shall perform the duties now performed by county clerks in extending taxes on the assessment books and such other services pertaining thereto.