Upon a showing by the person that DNA testing may be relevant to the person’s claim of wrongful conviction, the court shall appoint counsel for an indigent person as follows:

(1) The court shall first contact the chief counsel for the Commission on Public Advocacy to inquire if the commission is able to accept the appointment. If the chief counsel determines that the commission can accept the appointment, then the court shall appoint the commission pursuant to the County Revenue Assistance Act; and

(2) If the chief counsel declines the appointment because of a conflict of interest or the case would exceed the caseload standards set by the commission, then the court shall appoint an attorney licensed to practice law in this state with at least five years experience in felony litigation to represent the indigent person at all stages of the proceedings. Counsel appointed under this subdivision, other than the public defender, shall obtain leave of court before proceeding beyond an initial direct appeal to either the Court of Appeals or the Supreme Court to any further direct, collateral, or postconviction appeals to state or federal courts. Counsel appointed under this subdivision shall file an application for fees and expenses in the district court which appointed him or her for all fees and expenses reasonably necessary to permit him or her to effectively and competently represent the client. The court, upon hearing the application, shall fix reasonable attorney’s fees and expenses. The court’s order shall require that such fees and expenses be paid by the Commission on Public Advocacy from funds appropriated by the Legislature. Upon receipt of the order, the commission shall pay such fees and expenses in the full amount determined by the court.