Students remain a resident of their home state unless they take steps to establish permanent residency in another state. Attending college is considered a temporary absence. You would not count days as a student.
Massachusetts says “your legal residence is usually where you maintain your most important family, social, economic, political, and religious ties, and it depends on all the facts and circumstances per case, including good faith.”
In your case, that appears to be DC.
Learn about legal and residency status in Massachusetts
File a resident DC return and non-resident Massachusetts return. Only your MA W-2 income will be taxed by MA. You can claim a credit for any MA tax paid on your DC return.
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