From my understanding, if you have served any length of time
in military service then you are considered a veteran. You should answer the question based on your
understanding of being a veteran.
The information on the NC state tax return is being used
only to compile a report about how many veterans are filing tax returns in
NC. Answering the question is completely
voluntary and will not affect your tax return in any way.
(Note: In researching
the answer to your question, there was not a distinction between “veteran” or “active
duty” with regard to the question on the tax return.)