If you are from New York and are going to school in the District of Columbia, but still have a New York driver's license, a permanent address in New York, are registered to vote in New York, and do not intend in living in the District after you graduate, then you have not established domicile in the District. In that case, you are a New York resident who has a temporary assignment there. Students often are in this category.
If you were not a resident of New York, for instance, if you were an international student, then the 183-day-rule could apply. If you moved from New York, changed your driver's license to DC, changed your voter registration to DC, changed your permanent mailing address at the school to a DC address, you could declare domicile in the District and file a resident return there.
The District is reciprocal in taxes with all other states, so if you live in New York and work in the District, you can file a non-resident return in DC, then file a resident return in New York.
This TurboTax Help article has information about reciprocal states and shows the District of Columbia reciprocal with New York. Reciprocal states
This TurboTax Help article discusses residency status. state residency status
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