It is illegal to shoot a mountain lion unless it is attacking you, another person, family pet or livestock.

26-66-3. Open hunting seasons and bag limits for upland game birds and quadrupeds (f) There shall be no open season on Hungarian partridge, northern and southern flying squirrel, mink, moose, muskrat, beaver, otter, Canada lynx, harbor seal, pine marten, Indiana bat, black bear, fisher, bobcat and mountain lion (felis concolor).

Caracals are not native to North America. They are imported (legally in some states) as part of the exotic pet trade. It is illegal to possess a Caracal in Connecticut. The one I caught was being transported from Oregon to New Hampshire, but escaped when the owner stopped in Connecticut. I am sure that there are other ones in private possession in Connecticut as we have captured them in other parts of the state. When they get large (40lbs) and unfriendly, some escape and others are released by the owners without regard to what damage the cat will do in our environment.