Two men travelling in a BMW were killed, as was locally named mother-of-one Alison Clark, 43, from Elloughton, who was in a Peugeot. A third man remains in a critical condition..
Mrs Clark leaves a nine-year-old daughter.
Unconfirmed reports say the BMW drove at speed on the wrong side of the road on to the A63 before colliding head-on with the Peugeot.
The Independent Office for Police Conduct said they had launched an investigation into the collision on Monday night near the Melton and North Ferriby junction, following a referral from Humberside Police.
A statement said they had been notified that “police vehicles had been involved in a short pursuit at different stages prior to the incident.”
Humberside Police said their standards department reviewed incidents involving multiple fatalities and serious injuries to examine whether their actions may have contributed, directly or indirectly.
One of the vehicles “was involved in an incident with a police vehicle prior to the crash” and the case had therefore been referred to the IOPC.
They couldn't comment further on the details of the accident, as they were under the remit of the IOPC.
The force said their thoughts were with the families of those who died. Specially trained officers were in place to support relatives.