N.H. Rev. Stat. Ann. § 21-I:35

There shall be no physical examination or health statement required for coverage under either the permanent group life insurance or group hospitalization, hospital medical care, surgical care and other medical and surgical benefit programs; provided, however, that, if a state employee otherwise eligible fails to apply for any such insurance coverage within the time required by the insurance contract, the insurer may require that the employee submit satisfactory evidence of insurability as a condition for becoming insured.