Police Chief Don Engler said his department's investigation of the Tuesday shooting will take about a week. Results will be forwarded to the Gila County Attorney's Office for a decision on whether to prosecute anybody, he said.
"What we're taking a look at is the circumstances regarding the securing of the weapon" and how the boys were able to get ahold of it, Engler told The Associated Press. "We are continuing our investigation, and we haven't ruled out criminal charges at this point."
He said it was too early to say what recommendation his department might make to prosecutors.
The boys and their mother were visiting the 78-year-old neighbor in their apartment complex when the shooting occurred in a bedroom.
The brothers found the semi-automatic pistol somewhere in the living area where it was not in plain sight, the police chief said without elaborating. Neither adult knew the boys had the weapon, Engler said.
The boys were playing when they found the gun, police said. The weapon discharged, and the toddler was shot in the head.
Engler said the mother was just entering the bedroom when the shooting occurred and there was nothing she could do to stop it.
The younger boy was rushed to a hospital, where he was pronounced dead.
Names of those involved were not released.
Engler said he didn't know whether the 3-year-old grasped what he had done. "That'd be a difficult stretch for me to make that assumption," the police chief said.
However, he said the shooting was a tragedy that was felt by many in the community, including members of his department. Payson is about 90 miles northeast of Phoenix and has a population of approximately 15,000.
Engler noted many of the department's young officers have children of their own. "Certainly it's difficult for our officers in those circumstances," he told KPHO-TV.