A motorcyclist died in a crash shortly after another man was shot in the head.
A 42-year-old man is critically-ill after being shot in Upper Enham, near Andover, at 15:00 BST on Wednesday.
Hampshire Constabulary said a motorbike had failed to stop for officers investigating the shooting. A short time later a motorcycle crashed on the A343 near Hurstbourne Tarrant, killing the rider.
Police said they did not believe there were any remaining suspects.
Officers have not confirmed whether it was the same motorcycle and rider that had failed to stop.
Officers were initially called to MacCallum Road, Upper Enham, to reports of an assault but it emerged the victim had been shot in the head.
He remains in a critical condition in Southampton General Hospital. A 40-year-old woman was also assaulted and suffered minor injuries, police said.
The motorcyclist, a 34-year-old man, died at the scene of the A343 crash. His next-of-kin have been informed and formal identification procedures are ongoing.
Officers also attended a property in Enham Alamein as part of their investigation.
"While inquiries into the incident in Upper Enham are at an early stage, detectives do not believe there are any outstanding suspects in this investigation," police said.
Test Valley district commander Ch Insp Kory Thorne said: "We know residents in the Upper Enham and Hurstbourne Tarrant areas will have been concerned by what happened yesterday.
"They are likely to see a continued police presence in these areas while we investigate the circumstances."
Anyone with information about either incident is urged to contact Hampshire Constabulary.
The crash has been referred to the Independent Office for Police Conduct (IOPC).