D.C. Law is as follows:
D.C. Code § 22-4504 (2012)
§ 22-4504. Carrying concealed weapons; possession of weapons during commission of crime of violence; penalty [Formerly § 22-3204]
(a) No person shall carry within the District of Columbia either openly or concealed on or about their person, a pistol, or any deadly or dangerous weapon capable of being so concealed.
Most assisted opening knives are too small to be weapons. If your knife can be shown to be a tool, there's nothing to fear. If you've never been convicted of a violent crime, I wouldn't worry. I carry a 6-inch blade knife for protection all the time in D.C. It could be considered a dangerous weapon, but I don't commit crimes, so I don't care.
Bottom line, just don't carry a dangerous weapon. I've been a victim of violent crime, so I've determined never to be without some means of defense. But I use my knife as as tool and can prove it. Any tool can be a weapon, and if you have a clean record, you should be fine.
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See DC Code sec. 22-4514(b):
(b) No person shall within the District of Columbia possess, with intent to use unlawfully against another, an imitation pistol, or a dagger, dirk, razor, stiletto, or knife with a blade longer than 3 inches, or other dangerous weapon.