N.H. Rev. Stat. § 4:1

No state official who is not a classified employee shall be discharged or removed except for malfeasance, misfeasance, inefficiency in office, incapacity or unfitness to perform assigned duties, or for the good of the department, agency, or institution to which such official is assigned, according to the procedures set out in this section, unless otherwise provided by law. I. The attorney general, the governor, any member of the executive council, or the appointing authority of such official, may petition the governor and council for the removal of such official setting forth the grounds and reasons therefor. II. Upon receipt of a petition, the governor and council, by vote of 3 or more members of the executive council in concurrence with the governor shall accept the petition and schedule a hearing. The state official shall receive notice of the hearing at least 45 days prior to the hearing date. III. The governor and council shall conduct a hearing in accordance with this section. Upon conclusion of the hearing, a vote of 3 or more council members, in concurrence with the governor, shall be required to remove the state official from office. The governor and council shall provide written findings, including a time frame for removal, in support of a decision to remove an official from office. Failure to obtain the required vote and concurrence of the governor shall result in the dismissal of the petition. IV. The governor and council shall set a reasonable rate for the legal fees of parties. However, no official shall be entitled to have any legal fees paid by the state unless the attorney general determines that he or she is the prevailing party. V. The governor and council shall provide copies of their written findings to counsel for the parties involved, or to the parties themselves, if not represented by counsel. VI. A party may appeal the order of the governor and council by filing a petition in the superior court within 30 days of the date of the order.