At around 10.15pm on Friday, officers were called to an incident in Hampden Gardens, Aylesbury, during which it is believed a firearm was discharged from a vehicle towards a second vehicle.
No-one was injured following the firearm discharge.
Following this incident, both vehicles drove away and later collided with one another in nearby Church Square.
A 26-year-old man was then assaulted, resulting in him being taken to hospital, where he remains with life-threatening injuries.
A 54-year-old man from Aylesbury was arrested on suspicion of attempted murder and has now been released on conditional police bail.
Inspector Andrew Alexander, based at Aylesbury police station, said: “We are renewing our appeal for witnesses to either incident that occurred on Friday.
“We are particularly keen to hear from anybody who may have seen a silver coloured BMW 330i or a silver Nissan Almera in the area prior to this incident.
“Anyone with any information should call 101, quoting URN 1618 (24/5).
“Alternatively, you can call the independent charity Crimestoppers anonymously on 0800 555 111 or make a report online.
“We are continuing to conduct a thorough investigation into this incident and would like to re-assure the community that there will be an increased police presence in the area while our investigation continues.”