Newly released surveillance footage from inside the store shows the June 14 incident, in which Officer Salvador Sanchez shot 32-year-old Kenneth French and his parents while they were shopping.
French, described as developmentally disabled by his family, was killed in the shooting. His parents, Russell and Paola French, were wounded by gunfire and hospitalized.
Sanchez's attorney has said the incident began when the off-duty policeman was assaulted while holding his toddler son, and contended that Sanchez opened fire after being knocked to the floor.
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Riverside County prosecutors announced Wednesday that a grand jury could not find enough evidence to warrant a criminal prosecution and therefore they would not file chargers. But the French family wants the officer held accountable.
"I pray to God that no child or family comes in the path of Salvador Sanchez. We are deeply disappointed with the decision and will fight for justice," Paola said at a press conference the following day.
The man's parents required weeks of hospitalization and continue to require ongoing medical care for their injuries.
The family is expected to file a civil rights case against the officer and the city of Los Angeles sometime in the next 30 days.