Tamir Rice's mother, Samaria Rice, said her son received the air gun from a friend before playing with it in a city park last month.
That's where, according to police, officers pulled up next to Tamir in response to a 9-1-1 call, and shot him two seconds later as he reached toward his waistband.
Samaria Rice said police also put her 14-year-old daughter in a cruiser that day. She said her daughter told her she had been at a nearby rec center when Tamir was shot just outside.
"Somebody came and told her at the rec that your brother was shot, and she came running," Rice said, "and she told me that the police tackled her and put her in handcuffs."
Cleveland police have not confirmed that account, though chief Calvin Williams said he's looking into it.
"We know that people came on the scene of the incident and tried to actually run into the crime scene," Williams told reporters after a forum Monday night. "And that just can't happen, because people get in the way of the first responders." He added, "Whether or not she was handcuffed, we'll have to check into that."
At the press conference Monday morning, Rice's attorney, Benjamin Crump, referred to video of the shooting released last month that shows officers pulling up to Tamir.
"They're supposed to deescalate, not escalate a situation. And everything you see in that video escalated the situation," Crump said.
Crump is based in Florida, and has represented the families of several young black men and teens killed in high-profile cases, including Trayvon Martin and Michael Brown.
Police have said after an investigation, they will turn the shooting case over the county prosecutor, who says he'll present it to a grand jury .