An unarmed man who thrust himself into a confrontation between police officers and a knife-wielding assailant in a Brooklyn apartment died from a bullet wound to the back after the police opened fire, the New York City medical examiner said on Wednesday.

The man, Rafael Laureano, had pushed his way past officers to confront the assailant, Francisco Carvajal, who also died in the shooting on Monday.

“It looks like he was inadvertently hit,” Stephen Davis, the Police Department’s top spokesman, said of Mr. Laureano. He declined to identify the three officers who fired.

The police had initially said that Mr. Laureano was stabbed before officers arrived and that he died from those wounds. However, an autopsy on Wednesday found no stab wounds to his body.

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The chaotic scene began a little before 7 p.m., when Mr. Carvajal, 47, came to the apartment of his former girlfriend, Kathy Russo. At first she barred his entry, Mr. Davis said, and called her friend, Mr. Laureano, 52, who came to the apartment.

When Mr. Carvajal returned, she opened the door to tell him to leave, but he pulled out a knife and pushed his way in, Mr. Davis said. He said that Mr. Carvajal and Mr. Laureano grappled as Ms. Russo, 35, locked herself and her children in a bathroom.

At some point, Mr. Laureano fled. In the hallway, he met police officers — a sergeant and four patrol officers — responding to 911 calls of a woman being attacked with a knife.

Inside, Ms. Russo could be heard screaming as Mr. Carvajal hacked at the bathroom door, broke through one panel and reached inside. Ms. Russo knocked the knife from his hand, Mr. Davis said, and used it to cut his arm and chest. But Mr. Carvajal had a second knife, Mr. Davis said.

The police burst through the apartment door and Mr. Laureano rushed in before they could stop him, Mr. Davis said.

“Drop the knife, drop the knife,” officers yelled at Mr. Carvajal as he moved toward Mr. Laureano, Mr. Davis said. Then Mr. Carvajal turned to come at the police, Mr. Davis said, and three officers fired more than a dozen times, hitting both men.