Officers were pursuing the Jeep 4X4 from Coppull when it left the road, mounted the pavement and ploughed into a front window of a bookmakers in Market Street at Hindley, Wigan - next door to a shop called Bonkers!.
Lancashire Police Tac Ops say the occupants decamped from the stricken vehicle and ran off.
But forensic experts were later examining the car for evidence to identify the thieves.
Tac Ops tweeted about the incident: "Stolen vehicle sighted on the Coppull border last night.
"After a pursuit the vehicle crashed into this shop front, with the offenders managing to escape.
"Plenty of forensic opportunities left behind. #Bonkers."