N.M. Stat. § 66-7-311
When overtaking on the right is permitted.
A. The driver of a vehicle may overtake and pass upon the right of another vehicle
only under the following conditions:
(1)
when the vehicle overtaken is making or about to make a left turn;
(2)
upon a street or highway with unobstructed pavement not occupied by
parked vehicles of sufficient width for two or more lines of moving vehicles in each
direction; or
(3)
upon a one-way street, or upon any roadway on which traffic is restricted
to one direction of movement, where the roadway is free from obstructions and of
sufficient width for two or more lines of moving vehicles.
B. The driver of a vehicle may overtake and pass another vehicle upon the right
only under conditions permitting such movement in safety. In no event shall such
movement be made by driving off the pavement or main-traveled portion of the
roadway.