Atencio's family gathered in Phoenix and made the decision to take him off life support on Tuesday.
"It should be today sometime," sheriff's spokesman Lt. Justin Griffin said of the video Thursday morning. Griffin said he planned to release copies to the media after detectives gave him one.
The Maricopa County Sheriff's Office has been refusing to release the video for days, saying the investigation was still ongoing. It even refused to give a copy to the Phoenix Police Department, which was simultaneously investigating the fight because its officers originally arrested Atencio and were involved in the altercation.
An attorney for Atencio's family accused the sheriff's office of trying to derail the investigations.
"There is no reason why they cannot release that video," attorney Mike Manning said earlier this week. "We're concerned about it being destroyed. Because that's what the sheriff's office always does in cases like this...We want that digital video released right away."
Manning could not immediately be reached for comment.