Medicare will be paying for the hospital bills. Will Medicare be contacting my car insurance company?
You need to notify them if this was a collision that involved another individual, car or property not owned by you. If a claim is made and you fid not report it, the insurer may deny coverage, in which case you will be personally liable. It is possible that Medicare will notify your auto insurer.
You have a duty to contact your insurance company that is outlined in your own individual insurance policy. That having been said, you should definitely contact them. If you don't, they might use this failure to notify them as an excuse to deny coverage, saying that you "failed to cooperate." Contact them ASAP.