If you own a non-resident (or “foreign”) company and want to do business in DC, you probably have to register with the DC government.
This applies to all corporations (including professional corporations), limited partnerships and LLPs, and LLCs. Unincorporated entities (like sole proprietorships or general partnerships) do not have to register.
There are a few exceptions to the registration requirement, which you can find in the DC Code here. Most significantly, if you are just engaging in an isolated transaction in DC and will not be doing other transactions in the ordinary course of your business, you do not have to register.
Foreign companies doing business in DC must file a report every two years. They also need to maintain a registered agent in the District who can receive legal process on their behalf.