January 1, 2020 NH law, HB 399, mandating annulments for arrests or convictions for less than 3/4 of an ounce of cannabis for any offenses prior to September 16, 2017 became the law. This law amends RSA 651:5-b. This means that any conviction prior to the date that possession of cannabis was decriminalized shall be annulled upon filing a petition and filing fees. The idea behind simplifying the process of annulment is to attempt to undo the criminal records for citizen's convicted of possession of cannabis.
In order to get a possession of cannabis annulled you must go to the NH state judicial system website to get a petition to annul. At this point use the general annulment form but it is anticipated that the judiciary will likely create a special form for for marijuana cases in the future.