West Yorkshire Police said the vehicle had failed to stop for officers in the Sowerby Bridge area at around 2.30am today.
Its driver was detained by police after the car crashed into a wall on Cross Wells Road, Ripponden.
A traffic officer tweeted: "Vehicle failed to stop for the Calderdale Traffic car around Sowerby Bridge area. Driver tested positive for cocaine on a roadside drugs test after colliding with a wall. #operationalsupport #fatal4 #Team3"
Police said the driver remained in custody in Halifax this morning.