If the company is based in New York, and they took New York State Tax from your wages all year, it sounds like all your income is from a 'New York source'.
If you file a Part-Year Resident return for the state other than NY you lived in, and declare the income you earned while living there, that state should give you credit for the NY tax you paid on that income, so you should owe no tax to that state; you are simply reporting. Prepare this return before your NY return.
If your employer did withhold NY tax for you all year, your Part-Year Resident Return to NY will be straightforward. They'll tax all your income and hopefully the tax paid was sufficient so you don't owe (and may even get a refund).
Here's more info on Part-Year Resident Returns and FAQs for NY Filing Requirements, and Telecommuting.
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