Corona police said the off-duty officer was shopping Friday night, holding his young child, when he was "assaulted" by a man.
The officer shot and killed 32-year-old Kenneth French of Riverside and critically wounded two of French's family members.
French's cousin posted a picture on social media of French with the other shooting victims, who he identified as French's parents.
The cousin, Rick Shureih, claims his relatives have been made out to be suspects and the off-duty officer the victim.
Shureih posted on Facebook:
"I'm not keeping quiet about this! People need to know! This is my family! These are the victims of the Costco shooting the other night. My cousin Kenneth was killed and his parents, my aunt & uncle were also both shot and are in ICU. Do they look intimidating to you? Did he really have to shoot them all? 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! If anyone was a witness please get in contact with us."
Shureih described French as a "gentle giant" who was mentally disabled, he told The Press-Enterprise. He said French and his family were unarmed at the time of the shooting.
MORE: Off-duty LAPD officer fatally shot man at Costco in Corona, police say
The off-duty officer -- assigned to the LAPD's Southwest Station -- suffered minor injuries in the incident.
The shooting occurred at the store located at 480 N. McKinley Street. Multiple witnesses said they heard gunshots around 7:45 p.m. They said there was chaos after shots were fired. People ran to escape, but the doors were reportedly locked, which added to the panic.
Investigators have not said whether French was armed, nor has it released the name of the officer who was treated at a hospital and released.
Authorities say the off-duty officer is the only person who fired shots inside the store. It is unclear if the officer is currently on duty.
Officials in Riverside County are also conducting a separate investigation.
The family's relatives are urging anyone who witnessed the deadly encounter to contact them.