Officers attempted to pull the car over on the A59 at around 23.45pm on May 17.
The car was eventually brought to a stop on Blackgate Lane in Tarleton at around 1am by a police stinger that blew out three of the car's tyres, say police.
A woman was arrested at the scene on suspicion of being carried in a stolen vehicle and a man made off through gardens.
Video shows man in van wielding weapon in Preston city centre fight
Dramatic reduction in speed limit on major route into Preston through South Ribble
Lancashire Police investigate after man found critically injured outside Preston’s Harris Museum
Thunderstorms and heavy downpours of rain predicted to hit Lancashire as Met Office issues yellow weather warning
Ribbleton man Karl Bruney arrested by Lancashire Police after firearms incident in Preston
A spokesman for Lancashire Police said: "A car failed to stop for a patrol on the A59 late last night and we started to plan a tactical operation.
"We set up a stinger which stopped the car on Blackgate Lane and a woman was arrested.
"One man made off through gardens and the police helicopter and dogs assisted with a search.
"The man has not been apprehended."
Anybody with information can contact the police on 101.