N.H. Rev. Stat. § 264:32
Any person who became subject to the laws of this state as they existed prior to May 1, 1951, having to do with financial responsibility for the ownership or driving of vehicles, shall continue to be subject to such laws, except that if it shall appear to the satisfaction of the director either from his own records or from extraneous information which shall be supplied to him in such form as he may require, that a person, who has become subject to the operation of such laws solely as a result of involvement in any accident, had in effect at the time of such accident a policy of insurance or other prescribed form of proof of financial responsibility for such accident, then and in that event such person may be relieved from the liability of furnishing past and future proof of responsibility for such accident.
RSA 264:32
1951, 66:6. RSA 262:44. 1963, 330:1. RSA 262-A:68. 1981, 146:1, eff. Jan. 1, 1982.