Officials say the struggle may have lasted 30 minutes. She apparently went off the side of a cliff while struggling to get free. A passerby in the canyon below helped the victim call 911.
Deputies say she suffered some bumps and bruises, but did not break any bones in the fall.
The suspect took the victim's water bottle with keys attached and her car.
Authorities would not identify the 35-year-old woman because the suspect attempted to sexually assault her.
The suspect is described as a "transient-type" Caucasian male with no front teeth, wearing a black leather jacket and blue jeans, and not wearing shoes.
The suspect stole the victim's vehicle, a Toyota Land Cruiser.
Anyone with information related to this case was asked to call the Los Angeles County Sheriff's Lost Hills Station at (818) 878-1808.