I cannot fathom an 'adverse' situation with professional law enforcement...anywhere.
That said, I had to display my credentials to a Massachusetts State Trooper whilst boarding a private aircraft at Logan in May.
I taught at UMASS/Amherst for more than twenty (20) years and regularly interacted with on duty Massachusetts LEO's in that capacity. More than a few of those years were whilst I was carrying pursuant to LEOSA.
All said, I simply cannot imagine an 'adverse' interaction with professional LEO's. For the record, I have carried a gun pursuant to LEOSA in at least twenty-five (25) states since retirement. I have become involved in activities in which I identified myself as a gun toting person on more than a few occasions. Nary an issue...ever...anywhere.
Hope that answers your somewhat puzzling question.
Be safe.
PS: re Connecticut, I usually commuted to UMASS via Bradley International Airport...in Connecticut.