In short, Yes.
DC considers renting property to be a business function, no matter how few or many rental properties you have and whether that property or properties are owned by one person, a few people, a trust, or a business entity. This is why you have to obtain a business license to legally rent your property.
While you might pay your personal income taxes to your home state, business taxes can be levied by the jurisdiction where you are conducting business (in this case, D.C.), forcing you to pay taxes to that jurisdiction on the business income and this is why you would need to file the returns in D.C. and pay taxes.
RentJiffy’s thought: this arrangement where rental income is considered business income seems to be unique to D.C. We suspect this was intentional by design when the D.C. City Council implemented the law that included rental property as part of the business license categories in the late 1990s. You see, DC is one of the most transient places in the world. Almost 60% of residential homes are not primary residences, meaning most property owners are not D.C. residents. Thus, they would not report the rental income or pay taxes to D.C., so they would not get tax revenue. By considering it a business activity, D.C. ensures they get the income taxes on the rental income.