The red VW Polo crashed on Swine Lane near the junction with Long Dam Lane just after 9.30pm on Tuesday (Jan 18).
Police said ther crash happened shortly after the Polo "was sighted" by officers.
A West Yorkshire Police spokesperson said: "Three people were involved in the collision. One woman was taken to hospital with serious injuries, which have been considered life-threatening.
"The two other men involved were injured and taken to hospital for further treatment.
"Road closures remain in place while investigations continue.
"Due to the prior police contact, a mandatory referral has been made to the Independent Office for Police Conduct for further investigation.
"Officers are appealing to anyone who witnessed the collision or the circumstances leading up to it, to get in touch, particularly those who may have cash-cam footage.
"Anyone who has any information that can assist with the investigation is asked to contact 101, quoting incident 1684 of 18 January."