Authorities arriving to the scene heard the final gunshot, and found Nieto dead in the parking lot with an apparent self-inflicted gunshot wound.
Sheriff's deputies say the shooting appears to have been a domestic dispute.
Neighbors said they heard at least five shots fired. One neighbor pulled the woman inside his home and apparently shielded her as the man continued shooting.
The woman, whose name was withheld, was hospitalized with non-life-threatening injuries.
City News Service contributed to this story.