Yes. Most health insurance policies have a provision that requires you to pay the insurance company back the amount that they paid for your medical treatment from the accident. You should read your insurance contract to determine if it contains an indemnification provision.
Frequently, we are able to get the amount that our clients are required to reimburse the insurance company reduced. The easiest reduction to obtain is pursuant to CJ11-112 which provides for a reduction in many situations for attorney's fees for up to one third of the recovery. Reductions can also sometimes be obtained if there is a liability issue or there are limited funds available.
If you do not make a recovery by settlement or a verdict at Trial you do not have to pay your health insurance company back.