No, you don't. You have a 5th amendment right not to incriminate yourself. That means:

1. You must have committed a crime, which is not a given in a traffic accident.

2. You may not be coerced by the government into incriminating yourself. You are not protected from your property incriminating you. Imagine how absurd a world that would be: the government couldn't use a bloody knife as evidence of a knife attack because the knife was owned by the attacker.

Importantly, you'll also note that if you try not to provide evidence against yourself in civil discovery, you'll end up in a world of shit involving contempt of court.