The brothers and sisters were in a car in the driveway and were preparing to go to the boy's baseball game when the vehicle did not start. The mother went out to try to find out what was wrong with the car, authorities said.
The boy took a weapon from the car console and accidentally pulled it while his mother was outside, hitting his sister in the head, the sheriff's office said.
Emergency responders were called and took her to a hospital in the Atlanta area. Two days later, the detectives learned that the girl had died, the sheriff's office announced.
The detectives determined that no charges would be laid.
"It's just a really sad situation," the sheriff's Sgt. Ashley Henson said Saturday morning. "Based on all the evidence and the situation as a whole, we felt that charges were not justified in this particular case."
Sheriff Gary Gulledge said that "the hearts of his officers are breaking for this family and we hope God will put his healing hands around them during this difficult time".
"We want to remind everyone to leave their firearms unloaded and secure in a place away from children so that it will never happen again," Gulledge said in a press release.