Yes, you do. In fact, if your health insurance is through your employer (an ERISA Plan), you may have to pay them back 100% of what they paid. Technically, health insurance companies are entitled to the first dollar before even attorney fees and the cost of the case are paid. Though, most health insurance companies will negotiate a settlement for less than the 100%. If you had Medicare or Medicaid, they are also entitled to be paid back. A lawyers should help you negotiate this part of your case.
Let me help you through this difficult process.