The District of Columbia (DC), USA, is governed by the US federal government, but it also has a local government with significant autonomy.
Tags are free
If you think a question needs a district-of-columbia tag then you go ahead and add it. Tags exist to make searching easier and more tags are better than fewer tags.
There is space for 5 tags on a question - only 1,065 out of 16,095 questions currently (12 June 2020) use all 5 (6.6%). Adding a relevant tag where there is space is always a good idea. Replacing a tag with a more relevant tag is probably a good idea - consider if the tag you are proposing to add will help more people find the question than the tag you are proposing to remove will.
However, be aware that editing a question bumps it to the top of the active queue, if you are going to change several questions, please spread the edits out over time so the front page doesn’t get swamped with them.