From
http://www.dccourts.gov/dccourts/about/judiciary.jsp:
Designed as the city hall by architect George Hadfield, the Old Courthouse was completed in three stages between 1820 and 1849. His design for the city hall, influenced by the European Neoclassicism he had studied in Italy and England, won a competition in 1820. From the beginning, the building was intended to house both administrative offices and courts.