I live in Texas and I had a car accident a frew months ago. I was found at fault by my car insurance and the settlement covered my car expenses only. My health insurance covered my medical expenses but kept sending me forms to fill out about the cause of my injury.. after the 3rd attempt, I mailed the form back with the information required. To my surprise, I got a letter back telling me that I may have to pay back some of the expenses covered by my health insurance since I had a claim with my car insurance... Do they have the right to do that?

The medical coverage of your car insurance policy should pay for you medical bills, up to your limit amount. After that, then you Heath Insurance should kick in. If your car insurance has not covered any medical bills then yes they could be responsible for a portion and that would be recovered by your Health insurance.