Lt. Jim Gavin says the driver ran over the woman during an argument at about 2 a.m. Thursday.
Gavin tells KTLA-TV that the victim was caught under a front wheel and dragged nearly a mile before a patrol car spotted the situation. Officers chased and stopped the vehicle.
Gavin says the victim was pronounced dead at the scene. Her identity has not been released.
The woman driving the car apparently collapsed and was taken away on a gurney.