A 32-year-old man who was shot dead inside a California Costco by an off-duty police officer was non-verbal and had an intellectual disability that meant his mental capacity was that of a teenager, his family says.

Kenneth French, who was shopping with his parents at the time, was killed by the off-duty LAPD officer at the Costco Wholesale warehouse store in Corona on Friday night.

His parents, Russell and Paola French, were also severely injured in the shooting and they remained in intensive care on Monday.

Police say they now are gathering evidence and video footage as part of their administrative investigation into the unnamed off-duty officer.

They had initially said the officer, who was carrying his child at the time, fired at French in retaliation after claiming he attacked him.

It is not yet clear exactly what happened inside the store that may have led to the shooting.

French's family are now demanding answers into the deadly shooting, saying the 32-year-old was a 'gentle giant' who had never been violent in the past.

Kenneth French, 32, who was shopping with his parents at the time, was killed by the off-duty LAPD officer at the Costco Wholesale warehouse store in Corona on Friday night

His cousin Rick Shureih said French, who was non-verbal and non-aggressive, had a mental condition that had deteriorated in recent years.

'He was a gentle giant,' Shureih told the LA Times.

'He's never been violent in the past. He's always been very cooperative and kept to himself.'

French lived with his parents who had dedicated their lives to taking care of him, his family said.

Shureih said it was unlikely a verbal confrontation took place because Shureih no longer spoke.

'It could have been that he bumped into somebody but couldn't communicate the fact that he was sorry,' Shureih said.

Shureih would not go into detail about his cousin's mental health.

He penned a Facebook post on Sunday with a photo of French and his parents, saying they had been unfairly painted as suspects following the shooting.

'My cousin Kenneth was killed and his parents, my aunt and uncle were also both shot and are in ICU. Do they look intimidating to you? Did he really have to shoot them all?' Shureih wrote.

'I'm posting this picture because the stories on social media have made them out to be the suspects, and the off duty cop the victim.

'This is a family that was unarmed and was just grocery shopping. Truth will come out! I'm sure this was a misunderstanding that got escalated for no reason!'

Shureih said his family were in the process of hiring an attorney and trying to obtain the surveillance video and witness statements to 'make sure justice is done'.

French's parents, Russell and Paola French, were also severely injured in the shooting and they remained in intensive care on Monday. French lived with his parents (pictured together) who had dedicated their lives to taking care of him, his family says

Police say they now are gathering evidence and video footage as part of their administrative investigation into the unnamed off-duty officer. They had initially said the officer, who was carrying his child at the time, fired at French in retaliation after claiming he attacked him

Authorities remained tight-lipped on Sunday and have not responded to requests for comment about what provoked the Friday night confrontation and whether anyone but the officer was armed.

Police said the officer opened fire after French 'assaulted' him 'without provocation' as the officer held his young child.

Bullets struck both French and his parents. French's mother remains in a coma while his father's condition improved slightly over the weekend.

The LAPD will continue its internal probe as Corona police and the Riverside County district attorney's office conduct a separate investigation into the shooting.

The officer, who identity hasn't been released, was treated and discharged at a nearby hospital. The officer's child was not injured.

Police said the off-duty officer was the only one who fired shots in the store.

They have not said if French had any weapons or if the officer identified himself as police before firing.

The shooting prompted a stampede of frightened shoppers to flee the store and seek cover inside.

Witnesses said they saw a man arguing with someone in the freezer section when at least six six shots rang out.

Shrieks from inside the store were heard on video recorded by shopper Nikki Tate, who had stopped by with her daughter to pick up steaks and lobsters for Father's Day.

Police said on Saturday that the officer opened fire after French, of Riverside, 'assaulted' him 'without provocation' as the officer held his young child in Costco (pictured)

French was killed and his parents were injured. His parents remain in critical condition after being struck by gunfire. EMTs were spotted tending to someone in the aftermath of the shooting

Tate said Saturday she was by the meat section when she heard 'about six or seven shots'.

She dropped to the ground and crawled toward her daughter who was at the other end. They huddled until they were able to escape through a side door.

'I saw people and heard shots and my first thought was 'Jesus, is this another mass shooting?'' she said.

'I didn't know if this was a random thing or a domestic thing or if this was a mass shooting. Everything was happening so fast, I just wanted to get me and my kid to safety.'

In the video, her daughter says: 'Mommy, we need to go.'

Meanwhile, Christina Colis told the Riverside Press-Enterprise that she was in the produce area when she heard six to seven shots and hid with other shoppers in a refrigerated produce room. She said her mother saw people injured on the floor.

'I thought maybe someone dropped a bottle of wine, but then I kept hearing shots,' shopper Will Lungo told the Press-Enterprise newspaper. 'An employee came in and helped us out through the emergency exit.'

Witnesses told KCAL-TV that shoppers and employees rushed to the exits. The station reported that more than 100 people were outside the store at one point.

The shooting prompted a stampede of frightened shoppers to flee the store east of Los Angeles and seek cover inside

Police said purses, cellphones and backpacks were left inside the store as panicked shoppers fled

Police said purses, cellphones and backpacks were left inside the store as panicked shoppers fled.

Los Angeles Police Commission President Steve Soboroff said on Sunday that it is Chief Michel Moore's decision whether to put the off-duty officer on leave.

It is not clear if that has happened.

The department's policies allow off-duty officers to carry concealed weapons as long as they are authorized for on-duty use, according to the LAPD manual.

Joseph Giacalone, a professor at the John Jay College of Criminal Justice and a retired New York City Police Department sergeant, said it's justifiable to use deadly force even in a crowded store if the attacker has a weapon.

'If the guy pulled out a pocketknife and approaches him, game over,' Giacalone said Sunday.

Giacalone said video footage from Costco's cameras and shoppers' cellphones will be critical to the dual investigations.

While it's not unusual for police to delay releasing information such as an officer's name in a shooting for safety reasons, Giacalone said it's important to get details out as quickly as possible.

'People start filling in the timelines for you' in the meantime, he said.