The sentencing came after Razo admitted he torched his own car to collect insurance money.
He also admitted he made up a story about two men assaulting him in his driveway on January 31. He says he shot himself.
Razo was assigned to the LAPD's Hollenbeck station when he falsely reported the crimes. He has since resigned from the department.
LAPD Chief William Bratton called Razo a disgrace to the department. Bratton and L.A. Mayor Antonio Villaraigosa attended a benefit to raise money for Razo after he was shot.
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