N.H. Rev. Stat. § 604-A:3
A defendant for whom counsel is appointed shall be represented by counsel from his initial appearance before the court at every stage of the proceedings until the entry of final judgment. If at any time after the appointment of counsel the defendant is financially able to obtain counsel or to make partial payment for representation, the court having jurisdiction of the case may terminate the appointment of counsel or direct the application of the funds available to the defendant to meet the expense of representation, as justice may require. If at any stage of the proceedings, the court having jurisdiction of the case finds that the defendant is financially unable to pay counsel whom he had retained, the court may appoint counsel to represent him, as justice may require. The court having jurisdiction of the case may, in the interest of justice, at any stage of the proceedings, substitute one appointed counsel for another.
RSA 604-A:3
1965, 296:1, eff. July 1, 1965.