Can a car insurance company ask you if you have health insurance when you make a claim?

I was in an accident recently and the other insurance company asked me if I had health insurance. I was not at fault. Can they do that?
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They're probably just curious if your health insurance company may or may not come back to subrogate on the claim. If you get in an accident, get hurt, go to the doc, your health insurance picks up some of the cost, the car insurance pays for the balance right? Well in subrogation the health insurance may have the right to go back to the car insurer and get back what they paid out on the doctor visits caused by the accident. But it's between the insurance companies, not you. You shouldn't be affected by it in anyway. And usually the car insurer will only subrogate if it's a large enough claim which in most cases, it's not.
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