Law enforcement sources tell TMZ ... a man was driving last night near the intersection of Crescent Heights and Melrose Blvd. when he claims he was sideswiped by a Range Rover that was trying to pass him on the right.

According to our sources, when the SUV didn't stop, the guy called police and reported the hit and run.

But the guy didn't let it go there. According to our sources, he began to follow the SUV himself (which wasn't difficult because there was traffic). We're told cops responded to the scene and even dispatched a police helicopter to track the SUV, unsure of how severe the accident was.

When cops finally caught up to the Range Rover, we're told the driver was none other than Bynes ... who told police she had no idea she had struck another vehicle. Our sources say the damage to Bynes' SUV was so minimal, it is possible she didn't feel the accident.

Law enforcement sources tell us Amanda was very cooperative with police and cops had her exchange information with the other driver. We're told she was not given a citation and cops will not be investigating the incident further.