Yes. You will allocate the amount of income you believe was earned in New York (NY). The NY step-by-step section will allow you to allocate the amount of income that should be taxed to NY (Form IT-203-A if you are self employed). If it's strictly W-2 wages, then this schedule is not needed. For wages the income will be allocated on Form IT-203 from the TurboTax interview.
Since Florida (FL) does not have a state income tax, they will not provide a credit for taxes paid to another state.
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