Who is responsible for your health insurance while you are off work due to workman's comp injury?

That is a decision made by your employer. If you are receiving benefit payments from Comp, the only deductions permitted by law are court ordered payments such as Child Support. If you have a co-pay or a benefit you want to keep, you should either make your premium payment to the company or authorize the Work Comp Carrier to deduct it from your check. Check with your HR department and find out how long you will have until they cease your benefits.