Yes. I see 2 interpretations of your question. You should file a NY part year return either way.
1. You left NY, did not work there, did not have NY source income. You will file NY as a part-year resident and only claim the income actually earned in NY. If the state wants to investigate, you have moving paperwork and can prove that you did not live there.
2. You did still work and have NY source income. Therefore it is all taxable to NY. Since NH taxes interest and dividends rather than wages, you would not receive a credit on the state return.
For more from NY see here.
For more on entering states see: How do I file a part-year state return?
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