(CNN) The cousin of a man shot and killed by an off-duty police officer in a California Costco says his relative was nonverbal and couldn't have started the argument that allegedly led to the shooting, according to a report by the Los Angeles Times.

Police said the victim, identified by the Corona Police Department as 32-year-old Kenneth French of Riverside, assaulted an off-duty Los Angeles Police Department officer in an unprovoked attack before the shooting.

The officer, who was reportedly holding a young child while shopping with his family when French allegedly attacked him, shot and killed French and also shot two members of French's family, police said.

Corona police Lt. Jeff Edwards told reporters just after the incident that police believe the shooting resulted from an argument.

"From my understanding, from some people we talked to, there was apparently an argument inside," Edwards said. "Some type of argument and ensued into a gun shot."

Shooting victim Kenneth French (right) and his parents, Russell and Paola French.

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