There are many states that require different types of basic "No-Fault" car insurance so without knowing your specifics insurance coverages it is difficult to say if you would be covered for this hit and run accident.

If your No-Fault insurance policy only includes Personal Injury Protection (PIP) and property damage liability then your vehicle would not be covered. If you have uninsured motorist property damage (UMPD) as part of your insurance policy then normally damages caused by a hit and run motorist to your vehicle would be covered but you would have to check your policy to make certain.

Without UMPD you would need to carry auto insurance above No-Fault coverages such as physical damage coverages of collision and comprehensive to cover your own vehicle when it is damaged. Without any of these coverages listed above you indeed would need to find the at-fault party in order to place a claim through their liability policy for the damages they caused in this hit and run incident.