If I have insurance through work and an independent policy, can I make a workman's compensation claim on both?

Question Details:

I am insured through my job but have not informed them about a supplemental insurance policy. Can I put a claim in to the supplemental company without jeopardizing my work insurance? I had a minor injury at work and missed 6 days because of it. All of the doctor's bills so far have been covered by workman's comp. I used sick time to cover the days off.

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