If you move to Massachusetts and receive pension payments from your former states' public employee retirement plans, you can deduct those from your Massachusetts gross income if the former state doesn't tax income its residents receive from Massachusetts. See Other states' tax treatment of out-of-state government pension.
Since Connecticut will not withhold Massachusetts tax, you should make estimated payments.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"