A convertible Audi crashed on the A460 Cannock Road near the junction with Wood Hayes Road in Westcroft, Wolverhampton, at around 4am on Sunday.
The Independent Office for Police Conduct (IOPC) has launched an investigation and said the smash involved one car and happened after a "police pursuit".
Wood Hayes Road and the A460 Cannock Road were closed on Sunday morning as an investigation into the incident began.
On Monday, West Midlands Ambulance Service confirmed two men had died in the crash, while a third had suffered critical injuries.
The grey Audi involved left the road and ended up embedded in a hedge next to the A460, the main road which leads from Wolverhampton to Essington.
It was left with major front-end damage, including a smashed windscreen, and was recovered on Sunday lunchtime with leaves and branches still stuck in the car.
An unmarked Audi police car was parked nearby behind the cordon, where a blue screen had been put up as collision investigators examined the scene.
Some residents living on the Cannock Road, close to the Staffordshire border, were woken by emergency services arriving early in the morning.
Neighbours told of their shock and sadness at hearing two people had died.
David Ray, aged 73, said: "The flashing lights woke me up. I didn't hear a bang. There was plenty of police here and an ambulance.
"It's a shame, it's bad. We do get speeding up here but we haven't had an accident for four or five years."
Dave and Karen Foster live close to where a police cordon remained up on Sunday afternoon.
Mr Foster said: "It's awful. You don't expect it. We do get speeding down here."
Wife Karen said: "It's distressing, you don't want to hear it. It's really upsetting."
Another resident, who did not want to be named, said: "I slept through it. I woke up this morning and saw the police car and knew I wasn't going anywhere for a while."
An IOPC spokeswoman said: “We have begun an independent investigation following a referral from Staffordshire Police into the circumstances surrounding a road traffic incident on Wood Hayes Road, Essington, Wolverhampton at 4am this morning, following a police pursuit.
"The fatal collision involved one vehicle and two people sadly died at the scene.
“Our investigators have been sent to the post incident procedures and are carrying out an assessment of the circumstances and available information.
“Our investigation follows a mandatory referral from Staffordshire Police and is in its early stages.”
The A460 was shut in both directions from Old Hampton Lane up to Wood Hayes Road throughout Sunday morning.
A Staffordshire Police spokesman said: "Staffordshire Police responded to a serious collision on Wood Hayes Road, Essington, at around 3.50am this morning.
"The investigation is being led by the IOPC. It would be inappropriate to comment further at this time."