The collision involved a black Renault Clio and a black Hyundai i30 occurred just North of Harewood Bridge at around 2.25pm on Monday 19 May 2014.
An elderly man, who was a passenger in the Hyundai, suffered serious head injuries in the collision and was airlifted to Leeds General Infirmary for treatment. His injuries are described as life-threatening.
The driver of the Hyundai, a woman in her 50s from Leeds, sustained a back injury in the collision and was taken to Leeds General Infirmary where she remains in a stable condition.
Another passenger in the Hyundai, a woman in her 80s, is also in a stable condition at Leeds General Infirmary, after sustaining injuries to her shoulder and wrist.
The driver of the Renault, a 21-year-old man from Harrogate was not seriously injured in the collision.
The A61 remains closed between the A659 Otley Road and Swindon Lane as specialist collision investigators conduct their enquiries at the scene.
Officers are appealing to anyone who witnessed the incident to contact them with information.
Alternatively, information can be emailed to firstname.lastname@example.org
Please quote reference number NYP-19052013-0291 when passing information about this incident.