Do you have to reimburse a health insurance provider that paid for medical bills if you received a bodily injury settlement from your auto insurance?

If they have a Subrogation Clause (Section of Property Insurance and Liability Insurance policies giving an insurer the right to take legal action against a third party responsible for a loss to an insured for which a claim has been paid) in their contract (and most do).

The above answer is correct. What this means is you need to take this into consideration when deciding on a settlement. If your health insurance paid $50,000 in benefits and your attorney gets 30% of what he/she recovers, settling for $75,000 may sound nice but you will likely never see a nickel of it.