The collision involved an unmarked police car and a Vauxhall Corsa.
The two occupants of the Corsa, both women in their late seventies, sustained serious injuries.
The 79-year-old women was taken to the LGI has multiple injuries, including broken vertebrae and a punctured lung.
The other female occupant was taken to Harrogate District Hospital.
The female Police Officer driving the unmarked police car was taken to Harrogate Hospital with a serious, but not life threatening injury.
Anyone who witnessed the collision is asked to contact police on 101 or email MCIT@northyorkshire.pnn.police.uk
Please quote reference number 12180078208 when passing on any information.