The Sheriffs Office says he did not have a permit nor asked for one. He has a history of driving with no licence or insurance for years.
Now this is simply a comment by someone on that website. I have no knowledge if it is true or not.
https://theconservativetreehouse.com/2016/07/08/the-curious-case-of-philando-castile-falcon-heights-mn-police-shooting/
Minnesota LE is not permitted to publicly identify whether someone has a gun permit.