In one video, from the Wagner Houses in East Harlem, a man wearing a striped shirt, jean shorts and a Yankees cap is on the hunt for a victim. He ventures into the stairwell and lumbers up a flight of stairs. Finding no one, he returns to the lobby and takes up a post in the elevator.

As the doors begin to shut, someone approaches. He thrusts his arm out, and for a freeze-framed second, the gesture might have passed for courtesy: a man holding an elevator door open for a young woman. When the doors closed, the man, Marquis Phillips, began to sexually assault her, a crime for which he was sentenced a year ago to a term of 78 years to life in prison.

“When I watch this,” Chief Jaffe said, “I think, ‘How can people live with this amount of fear, just entering into their building?’ ”

Peter Cestare, a former supervisor in the Housing Authority police force, before it merged with the New York Police Department, noted that with the passing years, elevators remained particularly crime-prone even as the urban streetscape became safer, a result of improved street lighting, ubiquitous security cameras and the advent of cellphones, which have all made it easier to identify and catch muggers.

In elevators, on the other hand, Mr. Cestare, who commanded the elevator vandalism squad in the late 1970s, said: “You’ve got your victim contained in a box. As the bad guy, you’ve got complete control over the situation, and that’s really what you want if you prey on people.”

Eight days after the 13-year-old girl was assaulted in August, a man was robbed at gunpoint exiting an elevator inside the O’Dwyer Gardens Houses in Coney Island. And in July, a man wearing a floppy white hat showed a gun and took the pet parrot of a woman as she exited an elevator in the Morris Houses in the Bronx.

The potential for crime is something that Housing Authority tenants are keenly aware of, overshadowing other elevator problems: erratic stops, doors that close on fingers or feet, chronic breakdowns. Tanya Lopez, a 29-year-old mother of two, said she was always mindful about who might be riding alongside her in the Sheepshead Bay Houses in South Brooklyn. If a man she does not recognize is also waiting for an elevator in the lobby, Ms. Lopez said, “I just stay back and let them go.”