Can you keep a catfish (all species except bullheads) in New Mexico?

No minimum size, fifteen a day. The Animas and San Juan Rivers in San Juan County have no limit at all — not a water either of these two lakes is part of.

NMDOW source page

What we left out on purpose

• New Mexico's cold-water (trout and kokanee salmon) regulations, including the three-tier Special Trout Waters system (Red/Green/Xmas Chile Water), are not modelled here. Neither Ute Lake nor Elephant Butte Reservoir is a trout fishery or appears in the Special Trout Waters list — both are warm-water reservoirs, so this silo's New Mexico entry covers the warm-water table only.
• Special Summer Catfish Waters (2/day, 4 possession) and Trophy Bass Waters (2/day, 2 possession) are real exceptions to the statewide numbers, but apply only to a named list of small lakes and ponds that includes neither Ute Lake nor Elephant Butte Reservoir.
• The Animas and San Juan Rivers (San Juan County) have no catfish, striped bass, or pike limit at all — not modelled since neither river is a water this site covers.
• Eagle Nest Lake's no-limit, must-keep northern pike rule and Bluewater/Quemado Lakes' exclusive tiger muskie fishery are named-water specifics not relevant to Ute Lake or Elephant Butte Reservoir.