Yes, unfortunately, she would have to file a North Carolina Nonresident return then a Michigan Resident tax return. She will get a credit for taxes paid to North Carolina.
Thanks. A follow up question:
She made under $2,300.00 for the year. Since this amount doesn't exceed her tax exemptions will she still need to file a state return in either state?
It depends. I recommend filling out North Carolina, then Michigan if she had withholding.
First, presuming she had withholding in North Carolina, this will return her withholding.
Second, as a resident in Michigan, she is required to pay tax on all income. As a dependent claimed on your return, she must file in Michigan if her Adjusted Gross Income was more than $1,500. (see page 3 column 2, Who Must File a Return from the Michigan Instructions Book link below)
2019 MI-1040 Tax Book starting on page 10: your daughter still owes a state level tax on the income she earned. However, since North Carolina will refund the full amount, there is no offset. See page 14, column 1: