New York nonresidents are required to file if they have New York-source income and have adjusted gross income (AGI) over $8,000 for Single or $16,050 for Married Filing Joint, or if you had a net operating loss for New York State personal income tax purposes for the tax year, without having a similar net operating loss for federal income tax purposes. See the NYS website at this link for more details.
See page 49 of the Instructions for Form IT 203 at this link for more on the New York NOL provisions. If the losses on your LLC are not "suspended" as passive losses, you may want to use the NOL provisions to carry your LLC loss forward to a future year to offset income from that LLC.
Even if not required to file a NY tax return for this year, if your LLC has passive activity loss (PAL) carryforward amounts (which can be different that you federal carryforward amount reported on Form 8582); or other amounts being disallowed for the current year and carried forward; you may want to file a return to track these from year to year.
The TurboTax New York State tax return will include the capability to file the NY nonresident tax return.
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