It depends.
If you were a nonresident, you would only need to report the interest income if the income is derived from a "business, trade, profession, or occupation carried on in North Carolina".
If the income is strictly from investment income, you would not have a filing requirement.
Please see the attached link for more information on whether you have a filing requirement or not. North Carolina bases the requirement to file based upon whether you had to file a federal return and the amount of your federal gross income as well as the source of your North Carolina income.
North Carolina filing requirement
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