A previous version of the legislation, Senate Bill 38, was initially introduced in January 2019 in response to years of alleged problems with the Glynn County Police Department. That bill didn't advance, but it was revived after Arbery's death.
Travis and Greg McMichael were charged with murder and aggravated assault in May after video of the incident surfaced and the GBI opened an investigation.
"They should have arrested the McMichaels at the scene, and they did not," said state Rep. Don Hogan, a Republican from St. Simons Island.
The legislation now moves to the state Senate for further consideration.