Under state law, motorcycle passengers: Do you currently have car insurance? Insurance is mandatory to drive in Ohio Yes I have insurance. But please show me your best quotes. No, please help me find the best insurance. Question Under state law, motorcycle passengers: Answers Must wear a hat. Must wear a helmet. Are encouraged to wear a helmet. Are only required to wear a helmet if under 21 years of age. Explanation In Massachusetts, both motorcycle operators and passengers are required by law to wear helmets.