You'll enter that additional amount paid to NC in 2016 by clicking on the Federal Taxes tab, then Deductions & Credits, then scroll down to Estimates & Other Taxes Paid and click on Other Income Taxes.
You'll land on the Other Income Taxes screen, where you'll scroll down to the heading for Other Income Taxes Paid in 2016. Click "Start" next to the line that says Balance due on your 2015 state taxes paid in 2016 and follow the prompts. TurboTax will ask you for the amount and the state it applies to.