I live in Washington DC but my employer is based in NY. How do my state taxes work?

I know that I will have to pay NY state taxes because of how handles taxes based on my employer being there.

 

So I would first file a NY state non-resident tax form, and pay NY state taxes. Then I would file a DC resident state tax form. Is that correct?

 

Would I get credit in DC for 100% of the state taxes I paid in NY? I want to be sure I won't get double-taxed on the same income. 

 

Thanks in advance!