It depends, but he does probably still pay NY tax. Since he is active-duty military, his state of legal residence remains what it was when he entered the Navy: New York. New York tax law is a bit complex when it comes to military income, but here's a website that sums it up well: http://www.military.com/money/personal-finance/taxes/state-tax-information.html#NY. Unless he is maintaining a residence outside of New York, New York does tax his income. Here is an additional FAQ about Military residence: https://ttlc.intuit.com/replies/3302301
If he is stationed in another state, he does not file a tax return to the other state, only New York.
Tip: If he can legally establish residency in Washington state by having the DD Form 2058 accepted and processed by DFAS, he may find this advantageous. Washington has no state income tax.
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