Thank you for your answer. I had found that page already, but I have problems applying it to my situation.

Domicile: My visa expired and I moved out of the US for a few months. Is that enough to establish a domicile abroad? So far, I would argue yes, since I had no US address I was present at or could be reached at during this time.
Permanent place of abode for > 11 months: Not in this tax year, but the use of "year" versus "tax year" in the same sentence is confusing.

I would assume that this makes me a part-year resident, but the rules are not entirely clear to me.

I can not answer your question without additional information. How many days did you spend in NY? What is your state of domicile? Did you have income from NY? What kind of income did you have? Any taxes withheld from NY?

Thank you for your time.
I spent 5 months in New York on a traineeship visa and 2 months on an H1B. I had an income (wages) during both periods. New York taxes were withheld from this.
The other months I was not present in the country at all. My income during these months was exclusively from the country I was in.

You would only need to report any NY sourced income on an NY nonresident state income tax return.