I have to agree with mirabile_dictu on this point:
An armed officer with the authority to haul you off to jail, and ruin your entire day/week/month/year is in a position of power and you are at a serious disadvantage at the time of an arrest, or citation. The "permission" is meaningless in that situation.
He should evangelize enthusiatically while off duty and out of uniform. I don't think Jesus carried a sword when he invited people to be baptized, much less a Glock 9mm.
I believe we Christians gave up the spreading of the gospel by the sword quite a few hundreds of years ago. It didn't work out very well in the crusades, and doesn't now either.
You said "He should evangelize enthusiatically while off duty and out of uniform."
In the book of Mark chapter 16 verse 15 Jesus is quoted:
"Go into all the world and preach the gospel to every creature."
He doesn't say except when in uniform. He doesn't say except when armed. He doesn't say exept when it offends Druids or Muslims, or ACLU lawyers.