No. New Hampshire is the only state that does not require auto insurance by statute. But if your business causes an accident, you are responsible for the damage under the state’s financial responsibility law. Most businesses carry commercial auto coverage anyway.
https://gc.nh.gov/rsa/html/XXI/264/264-mrg.htm
https://www.dmv.nh.gov/tickets-accidents-or-restorations/insurance-requirements-sr-22