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The actor, who plays forensics expert Warrick Brown in CSI: Crime Scene Investigation, was arrested last month after he was discovered asleep in his parked car in Palm Springs, California.
Police said a patrol officer found the 41-year-old behind the wheel, "disoriented and possibly under the influence of alcohol and/or drugs".
He was released on $5,000 bail and has now been charged with three felonies for possession of a controlled substance.
He told Access Hollywood: “Obviously I am embarrassed to find myself in this situation, and I am profoundly grateful to everyone for their support. I have complete confidence in and respect for the justice system and will cooperate fully with any investigation.”
Dourdon - real name Robert Gary Durdin - will leave the CBS series at the end of the current season later this month.
He is due to appear in court on May 28.
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