Can I make a property damage claim?

Will the insurance company believe that your father hit your vehicle when there is no damage to his vehicle? Insurance fraud is always on the mind of insurance adjuster. I have no idea who you and your father are. I am not saying that you two are planning to commit insurance fraud. However, insurance fraud is pretty common. So, you and your father need to plan that his insurance company may look at insurance fraud. You and your father should also keep in mind that his insurer may cancel or not renew his insurance. Alternatively, the insurer may raise his premiums. Your father and you should look at all the pros and cons before deciding what to do.

As it's your dad part of the answer is what's going to go down the easiest. His insurance pays is the best for you. Or he can pay on his own.

You can indeed make a claim to the insurer of an at-fault party.