During one of the incidents, a crowbar thrown from a vehicle that officers were chasing hit the marked police car, nearly knocking off its registration plate.
According to West Yorkshire Police, members of its Roads Policing Unit pursued the VW Golf after it failed to stop at 12.18am yesterday in Prospect Road, Cleckheaton.
Police pursued the car and during the chase several items were thrown, one of which was a crowbar that caused damage to the police vehicle.
The Golf was later abandoned in a field in Drighlington and four people are believed to have fled the scene. Despite a search of the area police were not able to find them. The car is thought to have been stolen in a burglary in Leeds in early March.
The previous day, a marked Roads Policing Unit car had a brick thrown at it, nearly smashing its rear window.
Officers went to a report of a car driving erratically in Springroyd Terrace in the Girlington area of Bradford at 6.50pm. Police were investigating at the scene when the brick was thrown.
Pictures of the damaged police cars were later posted on Twitter by West Yorkshire Police’s Roads Policing Unit.
Inspector Joanne Field, who leads West Yorkshire Police’s Roads Policing Support, said: “Fortunately no officers were injured in either of these incidents, but they do demonstrate the dangers that officers in West Yorkshire are faced with every day.”