"Today, I am still without details of the investigations being conducted by various agencies," Harrell said in the release on Wednesday. "Because of the lack of clarity that remains and the unknown timing of when I will receive the results of the investigations, I have made the decision to place Chief Arredondo on administrative leave effective on this date."
On Tuesday, Texas DPS Director Steven McCraw said the local authorities could have responded to the shooting within three minutes. McCraw said the only thing stopping a hallway of dedicated officers from entering the school classrooms was the on-scene commander who "decided to place the lives of officers before the lives of children."
At a presser at the end of May, McCraw said that the person who made the decision - the commander in question - was the School District Police Chief. A US media reported identified him as Arredondo.
Last month, Texas authorities said Arredondo was not cooperating with the state's probe into the incident.
Earlier on Wednesday, Texas State Senator Roland Gutierrez is suing the state's Department of Public Safety (DPS) for access to records related to the elementary school shooting.
On May 24, an 18-year-old gunman opened fire inside Robb Elementary School, killing 19 students and two teachers.
Preliminary results of the probe into the shooting found that there were no law enforcement officers at the school readily available to engage the gunman. However, McCraw on Tuesday said there was a sufficient number of armed officers wearing body armor at the school three minutes after the shooter entered the building.