A shooting by an off-duty police officer inside a Costco in Southern California that left a 32-year-old man with disabilities dead and his parents injured was "completely unjustified" and prosecution of the officer should be considered, the man's family said in a statement.

In the statement Tuesday via their attorney, Dale K. Galipo, the family of Kenneth French said he was not a danger to anyone and was not carrying a weapon when he was fatally shot on June 14 while at a Costco in Corona with his parents, Russell and Paola French, both of whom were also shot.

Russell French is recovering from injuries he sustained, and Paola French remains in critical condition, the statement said.

"The family believes that shooting was excessive and completely unjustified because Mr. French was unarmed and posed no immediate threat of death or serious bodily injury to anyone," the family's statement read. "Moreover, according to his family, Mr. French was non-verbal and had an intellectual disability."

Kenneth French, 32, who was killed in a shooting by an off-duty Los Angeles police officer at a Costco in Corona, California, is shown with his parents, Russell and Paola French, who were injured in the shooting, according to French's cousin. Rick Shureih / via Facebook

Authorities have not identified the off-duty officer who shot the family.

Corona police said Kenneth French allegedly assaulted the officer without provocation.

An attorney for the officer said he was shopping in Costco with his wife and had his infant son in his arms when they were "both knocked to the ground."

"The officer was unconscious momentarily," attorney David Winslow said in a statement. "While lying injured on the Costco floor, he was unprotected and had no other option to defend himself and his son from further deadly attack."

Winslow said the "only option" was for the officer to use deadly force. "The entire situation is a terrible tragedy for all concerned," he said.

French's family said criminal prosecution against the officer should be considered.

"French’s family is particularly bothered by the fact that if anyone other than an off-duty police officer had shot three unarmed civilians in a Costco, that person would be in jail and facing criminal charges for murder," the family's statement read.

“There seems to be unequal treatment of police officers compared to other citizens when deadly force is used, causing death or serious bodily injury, which is a great concern to many members of the community,” Galipo has said, according to the statement.

A spokesman for the Los Angeles Police Department said the officer is with its Southwest Division and has been placed on administrative duty pending the outcome of an investigation into the shooting.

A cousin of Kenneth French has told NBC News that he was “mentally challenged” and a “gentle giant" who was not violent and had no previous encounters with police.

The cousin, Rick Shurieh, said he wasn’t sure if Kenneth French had ever been “fully” diagnosed but knew he was on medication.

“His motor skills are fine; it’s just something cloudy up there,” he said. "He’s never been violent with any of us."