Officer Breitkopf, a member of the Nassau police’s Bureau of Special Operations, which responds to shootings and other violent situations, arrived with his partner in an unmarked car about 10 minutes after the shooting of Mr. DiGeronimo and emerged from it, in plain clothes, carrying an M4 rifle, Mr. Carver said. The officers had radioed ahead to announce their arrival on the same radio frequency that the transit agency’s officers had been monitoring, Mr. Carver said.

Officer Breitkopf, who was wearing a badge on a chain around his neck, exchanged pleasantries with Nassau County officers across the street from the DiGeronimo house and said he was going to go up for a look, Mr. Carver said.

It is unclear where Officer Gentile was when Officer Breitkopf arrived.

According to Nassau County officers at the scene, Officer Breitkopf was wearing his rifle on a sling around his shoulder, its barrel pointed down along his right side and his hand against it to keep it from banging, Mr. Carver said.

“He doesn’t have his finger on the trigger, obviously, but he has his hand on the rifle to secure it to keep it close to his body,” Mr. Carver said.

While he was walking up the lawn, someone shouted, Mr. Carver said, citing witnesses’ accounts.

“Nassau cops that were at the scene said they did hear someone yell out, ‘Gun! He’s got a gun! Gun!’ ” Mr. Carver said. Some officers said the shout may have come from a man who had identified himself as a retired New York Police Department sergeant, but it may have come from someone else, Mr. Carver said.

“We heard the same rumor,” a spokesman for the New York City Sergeants Benevolent Association said.

A New York Police Department spokesman, Paul J. Browne, said he knew nothing about a retired city sergeant at the scene.

Little was known about Officer Gentile’s career. He joined the department in 2006, a spokesman for the transit agency said. His union declined to comment, and attempts to reach him on Monday were not successful. On Sunday, the Nassau County police commissioner, Lawrence W. Mulvey, said it was unlikely that he would be charged with a crime.

In a statement, the transit agency praised its “highly trained professionals” and their multiagency operations throughout its 4,700-square-mile coverage area in New York and Connecticut. The agency’s police department and the officer involved in the shooting “are fully cooperating with Nassau County Police Department’s investigation into the tragic accidental death of Nassau County Officer Breitkopf,” the statement said.