That is not what it says. It says anything used in the course of their duties. While it isn't a huge difference, that is a pretty decent amount of latitude. It says nothing about requiring the department to purchase it for them.
Within the "course of duties" is work related.
When they are off duty, they are no longer pursuing or within the course of their work related duties. When they are engaged within the course of your duties, then at that time, they are using equipment that is issued to them by their department. They cannot just take an AR off the shelf, put all the goodies they want on it, and throw it in their cruiser & it be hunky-dory.
When they are off duty, they can purchase any gun that they like, as long as it is legal in CT. The only thing LEO's have that we do not, is LEOSA, and that only allows carry where we are not permitted (and then again, I don't agree with it), interstate or otherwise.
They do not own the gun that is in the center console of their cruiser, or on their hip. They are given to them, to be used during their time working.
They cannot sell, give possession of, or otherwise transfer that particular gun to anyone at any given time. At the end of their employment, those arms are given back to the department.
They cannot own what we civilians cannot. Point blank, that is what it is. They have no more rights than you or I do.
Sometimes you just have to Cowboy Up.