There have been no charges against the father and son involved in the incident, former police officer Gregory McMichael and his son Travis. CNN has reached out to Gregory McMichael for comment, but he said he won't be commenting because he is under investigation.
"This is an ongoing investigation," the Glynn County Police Department said in a statement April 28, adding that it "continues to gather and provide information to the District Attorney's Office that the case has been assigned to."
Two district attorneys have recused themselves over possible conflicts of interest, one of whom wrote that Travis McMichael acted out of self-defense and their actions fell within Georgia's citizen arrest laws.
Attorney Lee Merritt, who is representing the family, told CNN Sunday "the decision to rely on the citizen's arrest statute is really a recent invention, prior to that they just simply said it was self defense." Merritt says now the men are trying to use the law to say they were trying to stop a crime.
"According to that law, you actually have to be observing the crime or be in the immediate knowledge of the crime," Merritt said. "The only thing they have ever said is ... that Ahmaud stopped by a house that was under construction and he looked through the window. We don't know if that happened or not, but even if that did happen that is not a felony that would invoke the citizen's arrest statute that would make this allowable."
'We expect action this week'
After the shooting, Gregory McMichael told police he saw the same man "the other night" and that he stuck his hand down his pants on that occasion, leading McMichael to believe he was armed.
After seeing Arbery jogging, McMichael then alerted his 34-year-old son, Travis, according to a Glynn County Police report.
"Travis, the guy is running down the street, let's go," McMichael said, according to the report.
The two grabbed a shotgun and a pistol and followed Arbery in their truck, police said. Travis McMichael, the driver, followed Arbery and then attempted to cut him off, the report said. Arbery turned around and began running in the opposite direction, the police report said.
They chased Arbery to a nearby intersection where they caught up to him, the report said.
"Stop, stop, we want to talk to you," Gregory McMichael shouted at Arbery, according to the police report.
Travis McMichael then exited truck with the shotgun, the police report said. His father told officers Arbery "violently attacked" his son, the report said, and they struggled over the gun. Travis McMichael fired two shots, the report said, and Arbery fell. Arbery was ruled dead by a coroner.
At best, the men had the authority to follow Arbery and send law enforcement to that location, Merritt said. The 911 calls show the dispatcher was asking the men what Arbery is doing that was of criminal concern, Merritt said.
"They didn't give any answer for that, they said, 'He's a black man running down our road,'" Merritt said.
Defenders of the men are also pointing to a shoplifting conviction in Arbery's past.
"The reference to ... alleged conduct from high school or shoplifting is absurd and has nothing to do with his murder," Merritt said.
He told CNN he and the family are looking for the district attorney to indict the men involved in Arbery's shooting.
"We expect action this week," Merritt said.