N.H. Rev. Stat. Ann. § 282-A:37

An individual shall be disqualified for benefits for any week or part of a week with respect to which he is seeking to receive or has received payments in the form of unemployment compensation, or payments supplementary to New Hampshire unemployment compensation, under any law of the federal government; provided, however, that there shall be no disqualification for seeking to receive or receiving unemployment compensation, or supplementary payments, under Chapter 85 of Title V of the United States Code.