The City Council agreed Tuesday night to sign two contracts with attorney Michael Gennaco to probe the death of 37-year-old Thomas and review the police department's policies and procedures.
Gennaco specializes in examining law enforcement agencies and is chief attorney for the Los Angeles County Office of Independent Review.
The decision to hire Gennaco came during a heated council meeting in which City Council members momentarily walked out on the angry crowd.
People speaking before the council asked that they resign. The six officers involved in the confrontation are on paid administrative leave and Fullerton Police Chief Michael Sellers is on indefinite medical leave.
The threat of a cyber attack on Fullerton's website from a group of hackers known as "Anonymous" angered over the death of Thomas failed to interrupt service on the site today, police said.
In a recent YouTube.com video "Anonymous" said it will "remove from the World Wide Web the site belonging to the Fullerton Police Department."
Fullerton Police say they've already thwarted several cyber attacks.
"This is a credible threat. We are taking it seriously and are responding accordingly," said Fullerton Police Sgt. Andrew Goodrich.
The Associated Press contributed to this report.