The police and state officials are examining a surveillance video that recorded the death of a 16-year-old boy at a private residential treatment center in Yonkers this week as staff members physically restrained him on the floor after a basketball game.

The boy, Corey Foster, who was a resident student at the center, Leake & Watts, became “unresponsive” about 8 p.m. on Wednesday, while three staff members were holding him down in an approved technique called “Therapeutic Crisis Intervention,” Meredith Barber, a spokeswoman for the center, said.

The staff members released their hold and began CPR as soon as they noticed the teenager’s state, she said, and called 911 as well as the center’s medical staff.

“As part of our cooperation with police in this investigation, we’ve provided a video of the event,” Ms. Barber said Friday. It was recorded by a surveillance camera in the gym, where 38 youths and 14 staff members had been playing basketball before the episode.