A blue Ford Fiesta and a blue BMW 1 series crashed on Otley Road at the junction with Cold Bath Road at about 7am.
The driver of the Ford, a local woman, was pronounced dead at the scene.
A police spokesman said the three men are still in custody.
Officers are appealing for anyone who witnessed the crash, or saw either of the vehicles involved beforehand, to contact them.
Anyone with information is asked to dial 101, select option 2 and ask for the Major Collision Investigation Team. Please quote reference number 12160146200.