Officer Evan Solano was named as the officer who killed Alvarez, 22, during a police chase in Portage Park shortly after 1 a.m. on March 31.
Early in the investigation, COPA made a rare recommendation that the department relieve Solano of his police powers.
Chicago police released body camera footage in April, as well as several other videos, which showed the last moments of Alvarez's life.
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The night of the fatal shooting, Alvarez cut through a gas station in Portage Park with Chicago police following him, according to officials.
Moments later, he was seen on camera running before allegedly tossing shopping bags as officers drove closer.
The police report stated it was an "investigatory stop" for a person with a gun. Officers then chased him through an alley for more than 30 seconds, leading to a residential street. A pistol then appeared to be in Alvarez's right hand and a "glowing" phone in his left.
"The video certainly suggests enough for the police to make a claim that it was reasonable," ABC 7 Chicago legal analyst Gil Soffer said when the videos were released. "It was a split second decision and that it was reasonable for us, but we also have someone who was shot in the back while he was fleeing, and wasn't aiming the weapon at the police officers."
As Alvarez is shot, a gun ends up a few feet away. A CPD photo of a 9 mm firearm with a 17-round magazine and laser sight was later released in connection with the incident.
Alvarez can be heard in the video asking police why he was shot.
Solano is also being investigated for a May 21 road rage incident in the 2900 block of Logan Boulevard, the I-Team previously reported. That incident was also caught on video.
Solano has been on the CPD force for six years and was initially placed on a 30-day administrative leave.