In the 15 minutes that followed, the captain is seen heading to a jail clinic, where she fashions a noose out of the inmate’s pants, twisting the legs and tying them together in a loop. She then places the pants on the floor and uses a digital camera to take photographs that the department said were eventually uploaded to the Correction Department’s incident reporting system.

The case is troubling “because there was a supervisor whose job it was to make sure that we follow the rules who manufactured evidence to help the people she supervises to break the rules,” Mr. Peters said. “That’s an attack not on an individual inmate, but upon the justice system and civil order.”

The Investigation Department referred the case to the Bronx district attorney’s office for prosecution in March and then raised it with prosecutors again in June in a letter. With any case referred to prosecutors, Mr. Peters said, there is a “careful review by a number of veteran prosecutors” at the department “who conclude that there is a criminal matter that can be prosecuted.”

Even so, last week Robert T. Johnson, the Bronx district attorney, declined to prosecute the matter.

The department’s inquiry into Rikers, which began in June, followed a stream of revelations published in The Times and elsewhere about serious problems at the jail complex. In the last nine months, one inmate, a mentally ill Marine Corps veteran, died in an overheated cell, while another died after being locked in a cell for seven days, naked and covered in feces.

In its four-month investigation, The Times found that inmates had suffered fractured jaws and eye sockets, wounds requiring stitches and severe head and back injuries during altercations with correction officers. Some were beaten by multiple guards, while handcuffed, and after suicide attempts, sometimes in full view of witnesses, including other inmates and medical personnel.