Authorities said the shooting happened around 4 p.m. in the 7700 block of Telegraph Road. They said a 28-year-old man and 28-year-old woman showed up at a Quality Inn earlier in the day.
They began hanging out and drinking at the hotel pool, authorities said, and were not registered guests.
At some point, the pair started fighting and the woman ran into the hotel to tell the employee that her boyfriend had stolen her purse.
The employees called 911 and Montebello police showed up. The woman then took off in her car, driving a short distance from the hotel.
Authorities said the woman ultimately turned around and drove back toward the hotel, aiming her car directly at a Montebello officer while her boyfriend was talking to him in the parking lot.
"She gets emotional - may have been drinking all day, who knows what else - and ends up driving her car toward the officer and her boyfriend. Bad decision-making all the way around," L.A. County sheriff's Lt. John Corina said.
The officer fired several shots to stop the car, and the woman was struck. She was taken to a nearby hospital, where she later died.
Authorities said no one else was injured in the shooting.
The investigation was ongoing.
Anyone with more information was urged to call the L.A. County sheriff's department homicide bureau at (323) 890-5500.