The usual way this works is that you complete your non-resident state first (NC) and then complete your home state (VT).
This will allow TurboTax to calculate the NC tax and then carry it to your Vermont return.
In the Vermont state interview, you will see a screen with the heading "Tax Paid to Another State or Canadian Province". Answer "yes" and you will begin a section of the interview in which you will enter certain North Carolina information into the screens (this is a good reason to have done NC first).
NOTE: you must file a form IN-117 for each state, so if you have other states in which you paid state taxes besides NC, when you come to the screen headed "Other State Tax Credit Summary", click on "+Add another State or Province" to add the next state.