Enter everything (income an expenses) from the rental on your federal return and when you go through the state return, TurboTax will give you the option to allocate the net income or loss to the appropriate state.
Here are the instructions for filing a nonresident return. Prepare the nonresident BEFORE your resident state. And be sure to note the rental state in the Personal Info section...All of that is detailed in the link!
@jatoc
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