It shall be the duty of the county assessor of any county embracing the whole or a part of any drainage district, to assess and enter upon his tax roll each year, the names of the owners, together with a description showing the area of each tract of land in any such district of his county, subject to taxation under this act N.M. Stat. Ann. § 73-8-1 to 73-8-60. Each such assessor shall deliver to the board of county commissioners of his county a certified list of all such entries containing the information aforesaid, and the assessor of any county in which shall be situated lands within the district other than the county wherein is located the office of the district, shall transmit to the county commissioners of the county wherein the office of such district is located a duplicate certified list of the aforesaid lands within his county. Upon receipt by each such assessor of notice from the county commissioners of the levies required to be made by the provisions of this act, he shall extend such levies upon his tax roll, to be collected in the same manner as other taxes.