If you pay the out-of-state fine no, points will not be assessed in Connecticut. If you fail to honor the ticket than NY will report that to Connecticut and Connecticut will suspend your driving privilege until the NY ticket is cleared and you pay Connecticut a restoration fee. NY is an expensive state to get a speeding ticket in; even more expensive if you don't settle it timely.
If you plead guilty or are convicted of a speeding ticket in another state, the state where you got the ticket may report it to the Dept of Driver Services in your home state. If they do, then you would be assessed points based on how your home state handles a ticket for that speed.