The incident happened in Carndonagh but only after it had been pursued through Moville and Redcastle.
The car was eventually stopped in Carndonagh after it struck a patrol car.
A young man, believed to be a juvenile was arrested at the scene.
He was released later and a file on the incident is being sent to the DPP.
A local Garda spokesman revealed that the two officers are lucky their injuries were not more serious.