D.C. Code § 20-525
A personal representative may resign by filing a written statement of resignation with the Register after giving at least 15 days written notice to all interested persons of intention to resign. If, within such 15 days, no one applies for the appointment of a successor personal representative or special administrator and no appointment is made, the resigning personal representative may apply to the Court for the appointment of a successor. Upon the appointment of such successor, the resigning personal representative shall immediately account for and deliver the property belonging to the estate to the successor personal representative or special administrator. The resignation of a personal representative shall be effective upon approval by the Court.
D.C. Code § 20-525