Officers were alerted at around 7.50am on Monday 17 December 2012 after a black car left the westbound carriageway at Bilborough and landed in a ditch.
The woman driving the vehicle suffered fatal injuries in the collision.
She has been named as Marzena Dajlanaj, aged 30, from York. The inquest into her death was opened and adjourned today (Wednesday 19 December 2012).
Both lanes of the westbound carriageway were closed for a number of hours while police investigated the circumstances surrounding the collision.
The A1237 was also closed to prevent vehicles trying the access the carriageway.
Officers are appealing to anyone who witnessed the collision to contact them with information as soon as possible.
Anyone who can help the investigation is urged to contact North Yorkshire Police on 101 – select option 2 – and ask for Traffic Sergeant Paul Cording or Traffic Constable Gemma Wood.
Please quote reference number NYP-17122012-0060 when passing information about this incident.