All members that operate sponsored vehicles must comply with all laws concerning vehicle registration, operator licensing, and insurance on any vehicles used official or unofficially by members in the state and locality in which they serve.
During your service you are covered by the Federal Tort Claims Act for third party liability, which relates to damage or injury to others only while performing official duties. Members are also covered by the Federal Employee’s Compensation Act for personal injury.
AmeriCorps is not responsible for any damage done to your own vehicle, so it is imperative that you maintain insurance on your personal vehicle.
See also:
What is the V-81 Transportation Form?
How do I get reimbursed for travel to do my assignment?
Why would I need to use a vehicle or public transportation?
Where can I find the V-81 Form?
What happens if you use more than one mode of transportation?