The incident happened Saturday night. Surveillance video shows a man walking toward the flag in front of the home on Welby Way, lighting it on fire and walking away.
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Investigators were considering the possibility of a hate crime because the homeowner is Jewish.
But police say the suspect, 31-year-old Kevin Miller was not motivated by hate.
Miller was arrested around 10:45 p.m. Monday. He was booked at Van Nuys jail for arson of an inhabited dwelling and bail was set at $250,000.
Police say Miller does not have prior arrests for arson. His possible motive for setting the fire was not disclosed in an LAPD statement.
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Nobody was home at the time of the blaze, but the homeowner spotted the flames after receiving a notification from her Ring camera.
She immediately called 911, but the fire had already spread to the lawn. Fortunately, a neighbor jumped into action.
"I saw the hose there and thank God it was right there... I pulled it as far as I could and I was able to put my thumb over it and start squirting at it... And then I went up on the roof and I just kept going and going and going until I didn't see any flames anymore," said the neighbor, Jeff.
The homeowner and the neighbor who put out the fire had not met until this incident. Residents described the neighborhood as a tight-knit community where everybody is willing to help each other.