Were you required to pay quarterly state estimated taxes throughout the year? If so, and even if your payments covered the full amount of tax liability when added up at year's end, if any one quarter was underpaid that can cause an underpayment penalty. I'm not saying that's what happened in your case--only describing one scenario where that can be seen. I don't know if the same is true for your state, but as an example, the Federal return has some "safe harbor" rules/exceptions and a way to annualize the income on the Federal penalty form to avoid or lessen an underpayment penalty. I don't know if NC has any of that or not. I'm a fellow user--not a tax expert--and a long way from NC.
If you have a copy of your state return with all the forms and worksheets, it may have a penalty form where that is calculated. That may give you a clue as to what occurred. A penalty figured by TurboTax is often subject to revision by the tax agency, since it doesn't always know exactly what specific date the payment is considered credited by the tax agency so may be calculating it differently. So occasionally the IRS or state will ask for more penalty, but even then, it might be avoided or lessened if one qualifies for one of the exceptions mentioned above.
Your NC letter may have contact info on it if you want to speak to the NC DOR. Otherwise, here's a way to find their contact page:
FAQ: How do I contact my state department of revenue?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-rev...
@TarHeelAlan
