The young man is said to be critically-ill after the accident involving his motorbike and a double decker bus near the junction of Thorpe Street and Boothtown Road last night.
Police say he was seen by officers on Thorpe Street, travelling towards Boothtown Road, at around 6.58pm and failed to stop for officers when requested.
The motorbike and bus crashed almost immediately afterwards.
A spokesperson for West Yorkshire Police said: "The motorbike rider, a teenage male, suffered serious injuries and was taken to hospital where he remains in a critical condition.
"Road closures were put in place at the time on Boothtown Road but have since been removed."
Anyone with information which might help with the police's investigation should contact Calderdale District Police on 101, or via the 101LiveChat function on West Yorkshire Police's website, quoting log 1380 of May 10.
The spokesman added: "Due to the involvement of a police vehicle in the circumstances leading up to the collision, the incident was referred to the Independent Office of Police Conduct."