N.H. Rev. Stat. § 408-A:5
The term of any credit life insurance or credit accident and health insurance shall, subject to acceptance by the insurer, commence on the date when the debtor becomes obligated to the creditor, or the date from which interest or finance charges accrue if later, except that, where a group policy provides coverage with respect to existing obligations, the insurance on a debtor with respect to such indebtedness shall commence on the effective date of the policy. Where evidence of insurability is required and such evidence is furnished more than 30 days after the date when the debtor becomes obligated to the creditor, the term of the insurance may commence on the date on which the insurance company determines the evidence to be satisfactory, and in such event there shall be an appropriate refund or adjustment of any charge to the debtor for insurance. The term of such insurance shall not extend more than 15 days beyond the scheduled maturity date of the indebtedness except when extended without additional cost to the debtor. If the indebtedness is discharged due to renewal or refinancing prior to the scheduled maturity date, the insurance in force shall be terminated before any new insurance may be issued in connection with the renewed or refinanced indebtedness. In all cases of termination prior to scheduled maturity, a refund shall be paid or credited as provided in RSA 408-A:8.
RSA 408-A:5
1959, 66:1, eff. June 22, 1959.