We can answer your question in two parts.
First, after looking into the matter, and reading the Colorado instructions for the Form 104PN, it seems like the full amount of your (federal) taxable interest income ends up on Line 6, while the amount on Line 7 is just that portion of the federal taxable interest income attributable to the time that you were a Colorado resident. (As that appears to be none, for you, then you can answer the TurboTax question as $0 here.)
Second, according to the Colorado Department of Revenue, an individual "must file a Colorado income tax return if during the year you were:
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A full-year resident of Colorado, or
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A part-year resident of Colorado with taxable income during that part of the year you were a resident, or
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A nonresident of Colorado with Colorado source income;
AND
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You are required to file a federal income tax return, or
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You have a Colorado income tax liability for the year."
Thus, a Colorado LLC would give you enough reason to have to file a Colorado state return, because you do in fact have Colorado-source income. However, how much, if anything, you would have to pay in Colorado taxes is another matter. But, there is still a legal filing requirement, notwithstanding.
Thank you for asking this question.
