If a car is stolen and has an accident within 24 hours is the car owner's insurance responsible?

Your insurance company should cover the risk.

Good question. Doesn't the answer depend upon each insurance carrier's T&C? Do individual state laws trump policy limitations?

This answer fully depends upon both the language in your policy and the laws in the state where you reside. However, in general if you car was stolen and the person who stole the vehicle is involved in an accident, your policy would cover any damage to your vehicle however you would not be held responsible to any damage caused to others as a result of that accident. Be prepared for a thorough investigation by both your company and the company for the person whose vehicle was damaged because of this accident. Unfortunately in my experience, too many people cause accident due to intoxication or other and flea the scene then create a story about the vehicle being stolen to avoid paying the penalty for both their crime and damages to others.

It also depends on whether you have full coverage insurance or not. If you do, then the above is correct, but if you carry liability only, they will cover damages to others property, but not yours.