The cousin of Oscar Grant is recuperating from a police-inflicted bullet wound in the same hospital where his cousin died after being shot by an officer three years ago.

Oakland Police have said very little about the Sunday night incident in which Tony Jones, 24, was shot in the lower back while running from officers after his vehicle had been pulled over for being associated with a robbery.

"The officer ran after the passenger, and discovered the passenger was in possession of a firearm. The officer discharged his firearm, which struck the passenger," police said in a statement, adding that a firearm had been recovered from the scene.

Jones' lawyer, Waukeen McCoy, said his client did not have a firearm and called the officers "negligent," accusing them of using "unreasonable force."

"[Jones] is 24 years old. He' a young guy and he started to run," McCoy told ABCNews.com. "He knew his cousin had gotten shot by the police before. He had grown up in an environment where he was afraid of police officers."

McCoy, along with Jones' mother, Bertrina Works-Grant, were denied access to Jones' hospital room for several hours by the Oakland Police Department, McCoy said, even though Jones was not under arrest and charges hadn't been filed.

"The police stopped me at the door and, meanwhile, he's in there loudly requesting to see his attorney," McCoy said.

After speaking with a supervisor, McCoy and Works-Grant were able to see Jones.

"I talked to my son,'" Works-Grant told ABC-owned station KGO-TV. "My son said 'Momma, the officers [are] lying. They watched me get out of the car. They watched me walk. They started speeding up and I took off running across the street. And when I took off running … I heard the gun go pow pow pow."

The Oakland Police Department did not return a message from ABCNews.com.

McCoy said he planned to seek unspecified damages on behalf of his client.

"There's a long way to go," he said. "There's a lot of young African-American men that are being stopped and shot by the police without them going through the protocol."

Oscar Grant, 22, was shot on New Year's Day 2009 by a Bay Area Rapid Transit officer on a platform in Oakland after he was one of several people restrained by officers responding to reports of a fight. Grant, who was unarmed, died from his wounds.

Officer Johannes Mehserle was convicted of involuntary manslaughter and served half of a two-year sentence.  The Mehserle verdict sparked riots in Oakland, where many wanted the officer found guilty of second-degree murder.

Mehserle testified during his trial he had meant to use his stun gun to restrain Grant.