New Jersey and Pennsylvania drivers can be fined up to $1,000 if snow or ice flies off their vehicles and causes damage or injury according to a report by CBS Philly News (video below). Also NJ drivers need to be extra careful because they could be hit with up to a $75 fine if they do not properly clear the snow and ice from their vehicles before driving.

The State of New Jersey's Division of Highway Traffic Safety page has a section dedicated to ice and snow removal, and it explicitly notes that "it’s the law in New Jersey." They stress that snow and ice from the hood, windows and roof from all vehicles need to be removed.

Friends have told me it was the law, but I've never heard of anyone being pulled over for it. Honestly, I like to clean my car after winter storms for better visibility while I drive. I also do it out of courtesy to other drivers. I have witnessed clumps of snow and ice launched off the roofs from other cars on the highway. It did not look safe. Now I know for sure, that it truly is the law to have a snow and ice free car.

You can read more about this law here