Conn. Gen. Stat. § 27-85: When allowances are not to be paid.

So much of this chapter as relates to separation allowances shall be inoperative whenever the United States pays to dependents of Connecticut soldiers, sailors or marines such separation allowances as are herein described and whenever such allowances by the United States are equal to or larger in amount than the allowances provided under this chapter. Whenever the United States pays to dependents of Connecticut soldiers, sailors or marines such allowances and the amount is less than the amount provided for in this chapter, the state of Connecticut, under this chapter, shall pay to such dependents only an amount equal to the difference between the amount of the allowance paid by the United States and the amount which would be paid under the terms of this chapter if no allowances were paid by the United States.