Officers first spotted the VW Golf in Oldfield Lane, Wortley, on Saturday and pursued the car when it did not stop.
They followed it to Strawberry Lane, where it was abandoned, and a 28-year-old man was arrested nearby. He was interviewed and released on bail pending further enquiries.
The arrest followed a series of unconnected drugs raids in the area, which were prompted by tip-offs from the community.
Controlled drugs and around 60 cannabis plants were found when warrants were executed at Tong Road, Mistress Lane and Ley Lane in Armley and at Billingbaulk Drive, Fairfield Street and Roseneath Place in Bramley last week.
A further 100 cannabis plants were found at an address in Hall Road, Armley.
Officers arrested a number of people for drugs production, assault and theft from vehicles. They also recovered items stolen from vehicles in Armley and Bramley, and arrested a man in linked searches.
Sergeant Chris Craven, of the Inner West Neighbourhood Policing Team, said: “Drugs cause significant damage both to the lives of individuals who take them and in our communities where they fuel crime and anti-social behaviour.
“We are determined to keep up the pressure on people who think they can get away with growing and dealing drugs in our communities and local people can continue to help us by passing on any information they have.”
Anyone with information on drug dealing activity in their area is asked to contact their local neighbourhood policing team via 101 or call Crimestoppers anonymously on 0800 555 111.