According to legal docs, obtained by TMZ, the 61-year-old famed director was pulled over around 2 AM in Ketchum, Idaho after cops say they saw him driving without taillights and failing to use a turn signal.

According to law enforcement, Bobby said the 2019 Mitsubishi Outlander he was driving was a rental, and he couldn't figure out how to turn on the taillights. The officer asked Bobby, who admitted he'd left a bar, if he had anything to drink. He said no, but the officer says he smelled booze ... and Bobby's eyes were bloodshot and glassy and his speech slurred.

He was asked to get outta the car and perform a field sobriety test but he refused ... which got him arrested on the spot. Cops booked him for misdemeanor DUI and released him after he posted $2k bond. This is his first DUI offense.

Bobby is one half of the famous Farrelly Brothers duo. He directed "Me, Myself & Irene," "There's Something About Mary," "Stuck On You," "Fever Pitch" and "The Three Stooges."

His bro, Peter, is also a director, screenwriter and producer who won the 2019 Best Picture Oscar and Best Original Screenplay for "Green Book."