Full-time resident of two states?

I am a resident of New York State but a student in Washington DC where I live more than half the year.  New York State would have me fill out my Washington DC return first (to pay taxes on Washington DC source income) and then fill out my New York return (based upon all income) but receive a credit based upon the Washington DC tax paid.

 

On the other hand, Washington DC has a statutory residency rule that seemingly applies because I live in Washington DC more than 183 days of the year.  Washington DC would have me fill out my New York return first (to pay taxes on my New York source income) and then fill out my Washington DC return (based upon all income) but receive a credit based upon the New York tax paid.

 

So, how do I handle these contrary instructions?

 

Also, what about income that is not sourced from any state, such as interest from a US-wide bank?  Seemingly both New York and Washington DC would have me attribute that income to them as part of filling out the second return (based upon all income), and never to the first-filled-out return (for income attributable to a specific state).  How does that affect the answer?