The crash happened on East Parade in Harrogate, near the entrance to the Victoria multi-storey car park, at 1.20pm on Thursday, May 17.
A silver Skoda Fabia estate car was exiting the car park, and a black Vauxhall Corsa was travelling along East Parade from the Odeon roundabout when the two vehicles crashed.
The driver of the Skoda, an 85 year old woman, from Harrogate, was taken to Harrogate District Hospital.
But North Yorkshire Police said she has since been transferred to Leeds General Infirmary with life threatening injuries.
The driver of the Vauxhall, a 30 year old woman, from Wetherby, was also taken to Harrogate District Hospital with minor injuries and was later discharged.
Officers investigating the collision are appealing for information and witnesses.
If you can help, please call North Yorkshire Police on 101, select option 2 and ask for Rob Roberts or email [email protected]
Please quote reference number 12180086388 when passing on information.