If you did not receive a 1099-HC, the Massachusetts Department of Revenue says:
You can call your insurer or your employer's human resources department or benefits administrator for help, if you get health coverage through your job. If your insurer or your employer is unable to assist you, please refer to the Benefits Required Under MCC section below to see if your policy meets these requirements. If your plan meets all of the requirements, you may certify that you were enrolled in a plan that met the MCC requirements during that time period. See the link to their site at the bottom.
If you were a part-year resident on MA, then MA is only interested in your insurance coverage while you were a resident. Enter the insurance info that applied while you were a resident. If you had insurance all the time you were a resident, you can answer that you had full-year coverage for the purposes of TurboTax's interview.