D.C. Code § 23-901
Any member of a duly organized peace unit of any State (or county or municipality thereof) of the United States who enters the District of Columbia in fresh pursuit and continues within the District of Columbia in fresh pursuit of a person in order to arrest him on the ground that he is believed to have committed a felony in such State shall have the same authority to arrest and hold that person in custody as has any member of any duly organized peace unit of the District of Columbia to arrest and hold in custody a person on the ground that he is believed to have committed a felony in the District of Columbia. This section shall not be construed so as to make unlawful any arrest in the District of Columbia which would otherwise be lawful.
D.C. Code § 23-901