N.M. Stat. § 67-11-4
The highway authorities of the state or of any county, city, town or village are authorized to so design any controlled-access facility and to so regulate, restrict or prohibit access as to best serve the traffic for which such facility is intended. In this connection such highway authorities are authorized to divide and separate any controlled-access facility into separate roadways by the construction of raised curbings, central dividing sections or other physical separations, or by designating such separate roadways by signs, markers, stripes and the proper lane for such traffic by appropriate signs, markers, stripes and other devices. No person shall have right of ingress or egress to, from or across controlled-access facilities to or from abutting lands except at such designated points at which access may be specified.
NMS § 67-11-4