Conn. Gen. Stat. § 31-291

When any principal employer procures any work to be done wholly or in part for him by a contractor, or through him by a subcontractor, and the work so procured to be done is a part or process in the trade or business of such principal employer, and is performed in, on or about premises under his control, such principal employer shall be liable to pay all compensation under this chapter to the same extent as if the work were done without the intervention of such contractor or subcontractor. The provisions of this section shall not extend immunity to any principal employer from a civil action brought by an injured employee or his dependent under the provisions of section 31-293 to recover damages resulting from personal injury or wrongful death occurring on or after May 28, 1988, unless such principal employer has paid compensation benefits under this chapter to such injured employee or his dependent for the injury or death which is the subject of the action.