The force saw the motorist, who was said to be drunk, attempting to leave the site of the crash in Shirebrook on Saturday, July 10.
He is thought to have misjudged his exit on a roundabout and instead drove his Audi straight into a bush and fence.
Officers located the driver walking away from the scene in just his socks.
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He was then arrested.
In a Twitter post, Derbyshire Roads Policing Unit wrote: “Shirebrook last night. Drink driver fails to negotiate a roundabout choosing instead to drive straight in to a bush and fence. Owner located walking away from the scene in his socks. Arrested. #Fatal4 #DontDrinkDrive”.
One social media user responded to the tweet, adding: “Saw the aftermath of this, just after it happened I think. Another car had stopped and the lads ran over.”