N.M. Stat. § 33-3-18
Counties without jails; arrangements with other counties.
In case any county in this state lacks a jail or proper place of confinement for its
prisoners, the board of county commissioners of that county shall make contractual
arrangements with other counties, municipalities or independent contractors for the
incarceration and care of its prisoners, and that jail so designated by any board of
county commissioners of any county not having a jail or other proper place of
confinement shall be the legal place of confinement of the prisoners of said county.