Hi @baumgartner-chuc . Yes, you will need to file form Form IT-203 Nonresident and Part-Year Resident Income Tax Return, however, you would not file as a "non-resident", but as a Part-Year Resident as you did actually domicile in NY during the tax year.
You are required to pay taxes to NY on income that you earned as a resident of NY, regardless of the source of that income. Your CA source income would therefore be potentially subject to being taxed in both CA and NY.
In order to prevent both states from collecting taxes on the same income, the state in which you are a resident - NY in this case - allows you as a resident to claim a tax credit on your NY State tax for the lesser of what you actually pay CA (net of any refund) or what you would have had to pay NY on that portion of your income. So if you had, say, $20,000 withheld in CA taxes, of which $1000 was refunded after you filed a CA return, you paid CA $19,000 in tax on your CA earnings, and you will be able to claim a credit of up to $19,000 on your NY return, depending on what you would actually have had to pay NY.
Regarding the income apportionment, yes, that is an acceptable way of doing it, using the formula you proposed, 5/12. If you know the actual amount earned during the time in NY, then that would be the preferred way of handling it should you ever be questioned by a NY taxing authority.
Finally, when using the Turbo Tax program, you would be filing a multistate return. First complete the CA Non-Resident return, followed by the NY Part-Year resident return. During the entries, the NY return will ask you both for the amounts earned in NY and also for the taxes paid in CA to calculate the correct amounts due.
I hope this helps 🙂
