As a student, I paid DC income taxes despite living in NYC. How would a tax return work in my case? Would I get a refund of my DC income tax and have to pay NYC taxes?

I'm a full time student in Washington DC and I ended up paying DC income taxes previously this year for about 2,600$ after taxes. Should I file a tax return? Would I end up getting my taxes back, and have to pay NYC taxes for that much earned?