N.M. Stat. § 1-5-4
County register; establishment.
The board of county commissioners shall direct the county clerk to establish a county
register. The county register shall be filed in fire-resistant containers in the county courthouse.
The files containing the county register shall be arranged to provide ready and convenient
access and shall be kept locked except when being used by authorized persons in accordance
with the Election Code [Chapter 1 NMSA 1978].