At 2.07pm on Thursday, West Yorkshire Police were called to a collision on Cemetery Road in Yeadon, near Leeds Bradford Airport.
It was near the road's junction with Haw Lane.
The crash involved a white Vauxhall Corsa heading towards East Carlton and a blue Citroën DS5 heading in the opposite direction.
Yorkshire Ambulance Service also attended the scene and dispatched an ambulance.
The passenger in the Citroen, a woman in her 70s, was rushed to Leeds General Hospital.
A West Yorkshire Police spokesperson said she suffered “serious injuries that are not considered life-threatening”.
It added: “The driver of the Corsa and another man were placed in a white Seat Leon and left the scene before emergency services arrived.
“The Corsa was later reported stolen in a burglary at Manor Close, Yeadon.”
Members of the public reported that the road was closed for several hours while the situation was dealt with.
Officers are investigating the crash and robbery and are appealing for information from the public.
Anyone who witnessed either incident or has information that may help police should contact police on 101 or use the contact options on the West Yorkshire Police website.
Please cite log number 843 of November 21st.
Full statement from West Yorkshire Police
“At 2.07pm yesterday, police were called to a road traffic collision at Cemetery Road, Yeadon, at the junction with Haw Lane.
“A white Vauxhall Corsa heading towards East Carlton collided with a blue Citroën DS5 traveling in the wrong direction.
“The passenger in the Citroën, a woman in her 70s, suffered serious non-life-threatening injuries and was taken by ambulance to hospital for treatment.
“The driver of the Corsa and another man were picked up by a white Seat Leon and left the scene before emergency services arrived.
“The Corsa was then reported stolen by a burglar at Manor Close, Yeadon.
“Investigations into the collision and robbery continue and anyone with any information should contact officers on 101 quoting log 843 of November 21 or online at www.westyorkshire.police.uk/livechat. You will be asked to contact us.”