'Bold and the Beautiful' Star HIT BY A CAR ... Both Legs Broken

"The Bold and the Beautiful" star Linsey Godfrey was run over by a car Monday in L.A. while she was walking down a sidewalk.

Cops tell us Godfrey was struck around 2:30 PM and got pinned underneath the car. When emergency responders arrived, a citizen had already moved her from the wreckage ... and she was rushed to the hospital by ambulance.

We're told the car that hit Godfrey veered onto the sidewalk after getting into an accident with another vehicle. Neither driver was arrested.

Cops say she suffered 2 broken legs ... and is currently in surgery.