N.H. Rev. Stat. Ann. § 592-A:2-b

Trial by jury shall not be afforded in the superior court for any violation as defined in RSA 625:9, except upon being subject to the imposition of a civil penalty which aggregates the total fines and penalties for a violation to an amount in excess of $1,500, in which case an appeal may be taken in the same manner as is provided for class A misdemeanor convictions under RSA 599:1.