When you are entering your information for the federal return in MY INFO it will ask if you made money in any other state. Choose VA from the drop down menu. When you are preparing your state returns, you will need to prepare NON-resident VA return first, and then prepare your NY state return.
NON-RESIDENT STATE RETURNS
Prepare the non-resident state return FIRST, then the resident state in order to get credit for the taxes paid to the other state.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/would-file-nonresident-state...
https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/file-nonresident-state...
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