I've never seen that movie. Seems like a long flowing scarf in a convertible would be the same trouble as long flowing hair. It would only fly around and slap you in the face!
Actually in the movie, she "drops" her scarf along the side of the road where she dumped the body of her lover the night before. She stops to get the scarf and is seen by the local policemen.
In a twist of fate, he's not really dead, but has temporary amnesia.
It's one of them bon bons and box of kleenex chick flix.