Officers asked the 25-year-old man to stop when he was driving on Butcher Hill on Tuesday, January 18.
The man did not stop and attempted to drive away from officers.
He then crashed into another vehicle and decided to try to run off on foot.
A large quantity of drugs and a machete were found in the vehicle.
The man was arrested.
A spokesman for the West Yorkshire Police - Leeds West team said: "On Tuesday 18th January 2022, officers from your Neighbourhood Policing Team were on patrol in the Kirkstall area when they had cause to speak with the driver of a vehicle on Butcher Hill.
"The driver wasn’t willing to hang around and attempted to drive off from officers before colliding with a vehicle and making off on foot.
"A large quantity of drugs and a machete were recovered from the vehicle and a 25 year old male has been arrested for possession with intent to supply, possession of an offensive weapon and dangerous driving."
Support the YEP and become a subscriber today. Enjoy unlimited access to local news and the latest on Leeds United. With a digital subscription, you see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Click here to subscribe.