N.H. Rev. Stat. Ann. § 546-B:47

A party or support enforcement agency seeking to modify, or to modify and enforce, a child support order issued in another state shall register that order in this state in the same manner provided in RSA 546-B:39 through RSA 546-B:46, if the order has not been registered. A petition for modification may be filed at the same time as a request for registration, or later. The pleading must specify the grounds for modification.