No, you don't file an IL nonresident income tax return since you earned income from a NY source not an IL source.
Per IL Department of Revenue: You must file Form IL-1040, Individual Income Tax Return, and Schedule NR, Nonresident and Part-year resident Computation of Illinois Tax, if you:
- earned income from any source while you were a resident,
- earned income from any Illinois sources while you were not a resident, or
- want a refund of any Illinois tax withheld.
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