N.M. Stat. § 77-1-9
Dogs; destruction.
A. Any peace officer may impound any dog found running at large unaccompanied
by and not under the control of the owner or handler, and further, the peace officer shall
destroy the dog if it is in the act of pursuing or wounding livestock or wounding and
killing poultry or attacking humans.
B. Any peace officer may kill any dog in the act of pursuing or wounding any
livestock or wounding or killing poultry or attacking humans whether or not the dog
wears a rabies tag required by Section 77-1-3 NMSA 1978. There shall be no liability of
the peace officer in damages or otherwise for such killing.