"My income did not exceed the standard deduction.
My employer did not withhold NY taxes from my pay or on my W2"
Q. Based in this, do I need to file?
A. Simple answer: yes.
You say "My income" did not exceed the standard deduction. You have two "my incomes" on the NY form IT-203, the Federal Amount and the New York State Amount. It's the NY state amount that gets taxed. But, it's the federal amount that determines whether you have to file or not. This is the way it works in almost all states.
https://www.tax.ny.gov/pdf/current_forms/it/it203_fill_in.pdf
