The incident happened Saturday evening around 9 p.m. in Beverly Hills, according to the Beverly Hills Police Department.
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It's unclear what prompted Edelman to jump onto the car but he did cause "damage," police added.
Police arrested him for misdemeanor vandalism, reports say.
Edelman was released on a citation and is scheduled to appear in court on April 13.
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The Patriots wide receiver was last year's Superbowl MVP.
On Instagram, Celtic's star Paul Pierce posted this photo of him and Edelman the same evening.