N.H. Rev. Stat. Ann. § 599:1-b

Any person aggrieved by a decision of a district or municipal court who was prevented from appealing therefrom, as provided in RSA 599:1 or RSA 599:1-a, through mistake, accident or misfortune, and not from his own neglect, may petition the superior court at any time within 30 days from the time the sentence is declared, to be allowed an appeal, setting forth his interest, his reason for appealing and the cause of his delay. The court may make such order thereon as justice may require.