State tax filing

My question is kind of the exact reverse of this.  I have lived in New York City for 20+ years.  I am considering entering into a consultant contract agreement for professional services  (1099) with a nonprofit entity domiciled in Virginia.  I will spend zero time in VA.  Will I have to file a VA state non-resident income tax form?  If so, do they credit the state income tax I will pay to NY?

 

Thanks, Bob