No, single-member LLC's are treated the same in New York as they are for federal purposes. Any income and expense from New York city sources would be reported as if the business was a sole proprietor and will be reported on your nonresident New York state and city personal return when you complete your individual tax returns.
Any taxes paid in New York can be claimed as a credit on your resident New Jersey tax return so you are not subject to taxes on the same income twice. Please see this FAQ for guidance on how to do this within TurboTax.
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