It your car was damaged by a hit and run motorist you should file a report with the police and contact your insurance agent. If the damage appears to have been done by another car you would file the claim under the Collision portion of your policy.
Collision coverage is for damage to your car when it hits, or is hit by, another vehicle or object. If you file a claim with your insurance company you will have to pay the deductible so if the damage is minor you may want to get an estimate on the cost of repairs to make sure it is more than your deductible amount. If the damage is less than your deductible then there is no reason to make a claim and thus you would pay out of pocket yourself to get it repaired.
We will go ahead and explain what your Comprehensive and Liability coverages are so you will know in the future when to use these coverages.
Comprehensive covers your vehicle, and sometimes other vehicles you may be driving for losses resulting from incidents other than collision. For example, Comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals. It also pays to fix your vehicle less the deductible you choose.
Comprehensive is also sometimes referred to as "other then collision" since it basically pays for damages to your vehicle caused by perils other than a collision, So while Collision insurance pays for damages your car sustained due to a collision with another object, Comprehensive covers damage to your automobile from such things as vandalism, theft, or glass breakage.
Liability coverages on a policy typically include Property Damage and Bodily Injury.
Property Damage Liability covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident. It also provides you with legal defense if another party files a lawsuit against you.
Bodily injury Liability covers other people's bodily injuries or death for which you are responsible. It also provides for a legal defense if another party in the accident files a lawsuit against you. Claims for Bodily Injury may be for such things as medical bills, loss of income or pain and suffering. Bodily Injury Liability covers injury to people, not your vehicle.
So your own Liability insurance could not be used in this hit and run situation where your vehicle was damaged. If however the driver and car were found that hit your vehicle then you would be able to make a claim under that car owner's Property Damage Liability coverage.
If your agent is not able to explain to you what to do in this situation or fulfill your car insurance needs, contact a CarInsurance.com agent and they can explain not only insurance terms and explain claim procedures but also tell you how they can get you the best rates.