D.C. Code § 24-211.06
The cost of the care and custody of persons confined in the said institutions charged with or convicted of offenses under any law of the United States not applicable exclusively to the District of Columbia shall be charged against the department or agency of the United States primarily responsible for the care and custody of such persons in quarterly accounts to be rendered by the Director of the Department of Finance and Revenue. The amount to be charged for such care and custody shall be ascertained by multiplying the average daily number of such persons so confined during the quarter by the per capita cost for the same quarter for all prisoners in the institution where confined, excluding expenses of construction or extraordinary repair of buildings. The sum so derived shall be credited to the current appropriation for the maintenance and operation of such institutions.
D.C. Code § 24-211.06