The collision happened on East Parade, Harrogate at the junction with the access road for the Victoria multi-storey car park at 1.20pm on Thursday 17 May 2018.
It involved a silver Skoda Fabia estate car, which was exiting the car park, and a black Vauxhall Corsa which was travelling along East Parade from the Odeon roundabout.
The driver of the Skoda, an 85 year-old woman from Harrogate, was taken to Harrogate District Hospital. 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 Rob.Roberts@northyorkshire.pnn.police.uk
Please quote reference number 12180086388 when passing on information.