NMDGF under big game rules and info:
Bow and Arrow
Bows include compound, recurved and longbows. Sights on
bows may not magnify targets or project light. Arrows must
have broadheads with steel cutting edges. No drugs may be
used on arrows. Arrows cannot be driven by explosives.
Crossbow and Bolt
Crossbows are legal for hunting big game species during “Any
Legal Sporting Arm” or “Muzzleloader” hunts unless otherwise
restricted. Sights on crossbows may not magnify targets or
project light. Bolts must have broadheads with steel cutting
edges. No drugs may be used on bolts. Bolts cannot be driven
by explosives.
That's too bad, I wanted to hunt turkey with stone this fall.
I guess I can still do primitive up to the tip, hand forged steel tips.
They don't list rabbit and ground squirrel as game and don't list any rules for taking them, just:
"Rabbits and Other Nongame Species
Common nongame species include coyotes, skunks,
rabbits and rock squirrels. Residents are not required
to have a hunting license to take rabbits or other
nongame species. Nonresidents must have either a
nonresident, nongame license or any current New
Mexico nonresident hunting license.
Nongame species may be taken on State Trust Lands
opened by easement by persons holding a valid
hunting or trapping license for protected species on
those lands during the individual's hunt or trapping
season. Nongame species may also be taken on
U.S. Forest Service and BLM lands open to hunting."
Meanwhile that's the same site that lists "any bow and arrow"