N.H. Rev. Stat. Ann. § 105-C:5

After the election and qualification of the police commissioners under this chapter, no chief of police, police officers, constables or superior officers shall be appointed in any town adopting this chapter except as provided in this chapter. Any chief of police, police officer, constable, or superior officer in office on the date the commission has been duly established, shall be deemed to have been appointed by the commission, subject to the terms and conditions of his original appointment.