New Mexico Statutes Chapter 19. Public Lands § 19-2-3. Taxation; civil process; concurrent jurisdiction

A. this state shall have jurisdiction to tax private persons, private transactions and private property, real and personal, resident, occurring or situated within such land or other area to the same extent that this state has jurisdiction to tax such persons, transactions and property resident, occurring or situated generally within this state;

B. any civil or criminal process lawfully issued by competent authority of this state or any of its subdivisions, may be served and executed within such land or other area to the same extent and with the same effect as such process may be served and executed generally within this state; provided only that the service and execution of such process within land or other areas over which the federal government exercises jurisdiction shall be subject to such rules and regulations issued by authorized officers of the federal government, or of any department, independent establishment or agency thereof, as may be reasonably necessary to prevent interference with the carrying out of federal functions; and

C. this state shall exercise over such land or other area the same legislative jurisdiction which it exercises over land or other areas generally within this state, except that the United States shall not be required to forego such measure of exclusive legislative jurisdiction as may be vested in or retained by it over such land or other area pursuant to this act, and without prejudice to the right of the United States to assert and exercise such concurrent legislative jurisdiction as may be vested in or retained by it over such land or other area.