Nyles Nelson, 51, was found dead of an apparent gunshot, according to a press release from the San Juan County Sheriff's Office.
Deputies were dispatched at about 1 p.m. Monday to a home at 21 County Road 3133 in Aztec.
A passerby spotted two bodies in the driveway. Police identified the people as Nelson and 24-year-old Erika Brown.
Police say they were a couple.
Evidence at the scene shows Nelson fatally shot Brown before he killed himself, according to the press release.
The investigation is ongoing, and a motive is not known.
Neighbors in the area told deputies they heard three or four gunshots around 3:30 p.m. Sunday. Police on Monday say that's when they think the shooting took place.