— the states shown in W2 forms

if NY is shown on W2 form then part of my income is withheld at NY tax department. If you do nothing then probably no refund from NY withheld amount.

— I don’t see any motivation to do this, but if I say my home address is foreign (HRBlock can take my foreign address)…..

I should still specify the same federal income as “nonresident state income”. If I specify $0 state income, then state tax payable becomes $0 and the entire state withholding tax would become refundable. This is unfair to the state and would likely raise a red flag.

However, if state withholding tax is $0, then I won’t bother filing state tax.

Your actual residential address — doesn’t matter. I could move from state to state.