Back in 1994, just over a year after the police commissioner at the time, Raymond W. Kelly, categorically banned officers from using the maneuver, a Bronx man named Anthony Baez Jr. died when an officer, enraged that a football had hit his patrol car, put Mr. Baez in a chokehold.

Image The city’s new police inspector general, Philip K. Eure, made chokeholds the subject of the first formal investigation by his office. Credit... Damon Winter/The New York Times

Two decades later, complaints about officers using chokeholds continue to flow into the independent city agency responsible for investigating police abuse. From 2009 to June 2014, the agency, the Civilian Complaint Review Board, found enough evidence to substantiate complaints against 10 officers accused of using the move on duty.

In July, the use of a chokehold emerged again, this time in the fatal encounter on Staten Island between Mr. Garner and Officer Daniel Pantaleo. The confrontation, much of it captured on video, provided a direct look at the potential effect of an officer’s arm being wrapped around a person’s neck.

The city’s new police inspector general, Philip K. Eure, appointed in May, made chokeholds the subject of the first formal investigation by his office, which was created by the City Council in 2013. His staff analyzed the 10 chokehold cases referred for discipline by the Civilian Complaint Review Board to the Police Department, and the report raised questions about the effectiveness of police training and the disciplinary process.

The endurance of the chokehold can be traced, in part, to the unpredictable nature of struggles between officers and the people they are trying to apprehend. That various types of neck restraint are widely used adds to the challenge.

“The thing about it is, if you do it correctly, it doesn’t result in injury,” said Harvey Hedden, the executive director of the International Law Enforcement Educators and Trainers Association. He pointed to the police in Kansas City, Mo., where officers developed the “lateral vascular neck restraint” — a kind of chokehold — meant to cut off the flow of oxygenated blood to the brain and render a suspect unconscious.

Even in places where chokeholds are banned, officers sometimes simply fall back on what works.

“For 20 years they’ve been frowning on the chokehold,” said Phil Messina, a retired New York City sergeant who now teaches self-defense tactics privately to officers. “What they forget is that they have a hundred-year tradition of the chokehold.”