I am a nonresident of NY, (live in another state the entire year), but I received lay off pay check from my company in NY and unemployement insurance from NY labor dept. In my case, do I have to pay NY tax?

If you neither lived nor worked in NY state, you would NOT be liable for NY state income tax, even if your employer is located in NY state.

Not sure that applies for the unemployment benefits, however, since they are sourced from NY state.