The 34-year-old victim, who was the front seat passenger in a silver Vauxhall Signum, suffered fatal injuries in the crash on the B7015 Sheephousehill Road in Fauldhouse, West Lothian.
The driver, who ploughed the car into a tree, disappeared after the accident and before emergency services arrived.
No other vehicle was involved in the collision, which happened at 7.45pm on Tuesday night close to the Sheephousehill Road junction with Breichwater Place.
The road is known for being a narrow countryside route without streetlights.
Sergeant Gary Taylor said: "We are appealing for any witnesses to the accident or anyone who saw the car prior to 7.45pm to contact us. We believe the vehicle had been heading westwards at the time.
"We are also keen to speak to the driver of the car who left the scene prior to the arrival of the emergency services."
The identity of the victim has not been revealed by police and it is not clear whether the car belonged to the driver.