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The man may be a transient, according to sheriff's deputies.
The 35-year old victim told deputies she had finished a run at about noon at Point Dume State Park and was standing at the edge of a cliff when she was grabbed from behind.
She says she and the man struggled for several minutes before she was able to break away.
That's when the woman ran and jumped off the cliff and slid about 100 feet down a steep hillside to the beach below.
A passerby in the canyon below helped the victim call 911.
The woman suffered some bumps and bruises, but did not break any bones in the fall.
Deputies say the suspect took the victim's keys and her white 2004 Toyota Land Cruiser.
Authorities would not identify the woman because the suspect attempted to sexually assault her.
Officials say the stolen Land Cruiser has California "Yosemite" plates, with license plate number 6CHF554.
The suspect described as a "transient-type" Caucasian male about 35-40 years old. He is about 5 feet 10 inches tall and 200 pounds, with a stocky build and no front teeth.
He was wearing a black leather jacket and blue jeans, but no shoes.
Anyone with more information about the attack was asked to call the Malibu/Lost Hills Sheriff's Station at (818) 878-1808.