If a friend is in an accident in your vehicle normally your insurance is primary and if your limits are exceeded the driver's auto insurance may be used as excess or secondary insurance.

No fault insurance typically refers to bodily injuries and not property damage so it sounds as if instead you would be placing a claim against your collision coverage. If this is the case then your insurance rates may go up since a claim is placed against your policy and thus the insurance company is paying out on your behalf.

In most states if you are not at fault then you can place a claim against the at-fault party’s property damage liability coverage for the damages to your vehicle. You should also notify your insurance company and you can file it against your physical damage coverage. So determine if this is possible by speaking to your insurance agent. For more information on your state's insurance laws contact your state's insurance regulator.

The typical rule is that if the repair cost is more than your deductible, then any premium savings you may see from not filing it with your carrier will be less than the cost you will have to pay for repairing the vehicle yourself (in most situations).