They said 45-year-old Johnny Davidson has been booked into the San Juan County jail on suspicion of second-degree murder and shooting from a motor vehicle.
It was unclear Sunday if Davidson has a lawyer yet who could speak on his behalf.
Farmington police told the Daily Times that officers were dispatched Friday night after Davidson allegedly called 911 and claimed to have shot a man.
They said the victim was later located with a single gunshot wound to his chest.
The man was taken to a hospital where he died of his injuries.
His name hasn’t been released yet by police.