The four centers cited in the report are the Lansing Residential Center and the Louis Gossett Jr. Residential Center in Lansing, and two residences, one for boys and one for girls, at Tryon Residential Center in Johnstown.

Officials at the centers also routinely failed to follow state rules requiring reviews whenever force is used, the report said. In some cases, the same staff member involved in an episode conducted the review of it. And even when a review determined that excessive force had been used, the staff members responsible sometimes faced no punishment.

In one case, a youth counselor with a documented record of using excessive force was recommended for firing after throwing a youth to the ground with such force that stitches were required on the youth’s chin. But after the counselor’s union intervened, the punishment was downgraded to a letter of reprimand, an $800 fine and a two-week suspension that was itself suspended.

The federal inquiry began in December 2007 following a spate of incidents at some of the 28 state-run juvenile residential centers, which house about 1,000 youths.

In November 2006, an emotionally disturbed teenager, Darryl Thompson, 15, died after two employees at the Tryon center pinned him down on the ground. The death was ruled a homicide, but a grand jury declined to indict the workers. The boy’s mother is suing the state.

During the same period, a separate joint investigation by the state inspector general and the Tompkins County district attorney found that the independent ombudsman’s office charged with overseeing youth prison centers had virtually ceased to function. In a report by Human Rights Watch and the American Civil Liberties Union issued in September 2006, New York’s youth residential centers were rated among the worst in the world.

Those scandals spurred a drive within Ms. Carrión’s department to overhaul the system. It reconstituted the ombudsman’s office and issued clearer policies on the use of physical force, leading to a sharp drop in instances where restraints were applied.