Kent Police was called at around 1am on Thursday 7 October to a report that a man had been found with injuries in Caxton Road, Garlinge.
The man, who was in his 30s, was flown to hospital by air ambulance but later died from his injuries.
The man's injuries were initially treated as having resulted from a collision with a vehicle. However, further enquiries have suggested the man may also have been assaulted before the collision.
Three people have since been arrested in connection with the incident. One man has been released under investigation and two others have been bailed while enquiries continue.
House to house enquiries have been conducted and police are keen to hear from anyone who may have information about what happened.
They are also asking residents to check doorbell camera and dashcam footage to see if they contain anything that could assist the investigation.
Anyone with information can submit it at the following link: mipp.police.uk/operation/4601020121F14-PO1
You can also call the independent charity Crimestoppers anonymously on 0800 555111 or complete the online form available via their website.