Spokeswoman Jessica Mayorga says four people were trapped when the beam fell Monday morning at the planned air conditioning center on Winchester Avenue.
A Yale-New Haven Hospital spokesman says two men being treated there are in critical condition and one is in serious condition.
A fourth person is being treated at the Hospital of Saint Raphael for injuries considered not life-threatening.
The federal Occupational Safety and Health Administration (OSHA) and New Haven officials are investigating.
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