Yes. If you are a Medicare beneficiary you may use your insurance to pay for medical bills, depending on the treatment required. Usually, your car insurance will pay their part first, and Medicare would pay afterwards for covered services. This also applies if you receive Medicaid benefits.
Now, if you are involved in an auto accident, you must report it to Medicare regardless of whether you intend to file a claim. This is important because Medicare must be reimbursed for the monies it spends on your medical care that resulted from the accident.
Keep in mind that Medicare will continue to monitor your claim after the accident. They will assert their right to recover any settlement money you receive to compensate itself for the money it spent on your medical expenses.
Generally, you are responsible for your expenses even if you were not at fault. Therefore, having insurance is important because it will offset your out-of-pocket responsibilities. If you were not at fault, the other party may not be liable for your medical expenses unless it was required through a settlement.