D.C. Code § 9-202.11
When an objection is filed with the Mayor as provided for in § 9-202.10, the Mayor shall institute a proceeding in rem in the Superior Court of the District of Columbia for the closing of the street or alley, or part thereof, and for the ascertainment of damages and the assessment of benefits resulting from the closing. The proceedings shall be conducted in the same manner as proceedings for the condemnation of land for streets and alleys pursuant to Chapter 13 of Title 16. Any damages awarded by the Court shall cover the administrative costs of the proceedings and shall be paid by the applicant for the closing, the applicant having the right, within a reasonable time to be fixed by the Court in its order confirming the verdict, to abandon the proposed closing without being liable for damages ordered by the Court. If no damages are awarded by the Court, the person who filed the objection shall pay the administrative costs of the in rem proceeding.
D.C. Code § 9-202.11