A man was taken to hospital following the incident outside Fever nightclub in Cannock at around 3.30am on Sunday.
A convertible Audi was then involved in a crash five miles away on a main road on the outskirts of Wolverhampton, having been pursued by police officers.
The Independent Office for Police Conduct (IOPC) said the convertible Audi was chased for a "short time" by police before it crashed into a telegraph pole and tree on Cannock Road in Westcroft, near Essington, just before 4am.
Will Craddock and Kaya Morrison-Taylor, both 22 and from Walsall, died in the crash.
A third man, named by friends and family on social media as Alfie Peakman, also 22, was critically injured and remains in hospital.
West Midlands Ambulance Service said medics were sent to treat a man who was injured following an assault near Fever, which is across the road from the police station.
A spokeswoman said: “We were called at 3.34am on Sunday to reports of an assault on Wolverhampton Road, Cannock.
"We sent two ambulances to the scene. On arrival, crews discovered one patient, a man, who was injured. He was assessed at the scene and conveyed to hospital for further treatment."
The IOPC, which is leading the probe due to the involvement of Staffordshire Police officers chasing the car before the crash happened, said its investigation remained at an early stage and that a review of police body-worn footage had begun.
IOPC regional director Derrick Campbell said: “Our thoughts are with the men’s family and friends, and all those affected by this tragic incident.
“We have contacted both families of the men who died to explain our role and how our inquiries will progress.
“There is a mandatory requirement for forces to refer to us incidents like this which result in death or serious injury and our investigation will thoroughly examine the circumstances of the police involvement and whether appropriate policies and procedures were followed.”
Tributes have been left at the crash scene in memory of Mr Craddock and Mr Morrison-Taylor, while thousands of pounds has been raised in their memories.