Hollywood seems to love this cliche, since I’m hard-pressed to think of a police flick that doesn’t involve the hero snatching some passerby’s vehicle and then wrecking it in the invariable breakneck chase scene. But is their any federal/state/local ordinance that permits an officer to temporarily “borrow” your automobile? Sounds like a flagrant violation of the fourth amendment.
Snopes has an article on this.
In brief, it would depend on your state laws regarding the doctrine of posse comitatus, which is basically the legal principle that you have an obligation to assist a police officer if he is in the middle of a hot pursuit of a suspect and asks for your assistance. Whether that obligation extends to letting him borrow your car would depend on the wording of your state law (I’m assuming that every state has some sort of posse comitatus law, which may or may not be the case). Apparently in California, according to Snopes, no one has ever been prosecuted for failing to let a police officer borrow their car, probably because it’s such a rare situation to begin with, and so it’s unclear what the court system would think of it.