Reported he was angry with the director and/or cinematographer who wanted another take on the scene they had just filmed. He was told the gun he was handed was "cold" (no live fire) so being pissed, pointed the gun at them and said "how about I shoot you" and fired. Only one shot, went through and killed the woman, and hit the director in the shoulder.
Whether he's charged and prosecuted in liberal Santa Fe County for his action is questionable.
You know what’s fascinating, if Balwin had not done that little temper tot routine, during the live filming, the real round would have just traveled out into the New Mexico landscape for several hundred yards and no one might have ever known.