N.M. Stat. § 73-20-48
Agencies, instrumentalities and political subdivisions of this state having jurisdiction over or charged with the administration of public lands situate within the defined geographical area of any district shall cooperate to the fullest extent with the district's supervisors in effectuating district projects and programs. Supervisors shall have free access to enter and perform work upon state public lands lying within their districts; provided, however, supervisors shall not have unqualified access to state public lands that are subject to private dominion under lease or that are developed for, or devoted to, another public use. County clerks of the counties within which all or a part of the district lands are located shall provide advice and assistance with conduct of elections and referenda.
NMS § 73-20-48