Police in the neighbouring French region of Haute-Savoie made the request to their colleagues in the Swiss canton of Valais, where on Wednesday the gunman went on a shooting spree, a police spokesman told AFP.
"French police in Haute-Savoie, who are wondering about a possible link between this killing and unsolved homicides in the region in recent years, have made this request," he said.
The gunman, known to have psychiatric and drug problems, killed three women and wounded two men in the tiny village of Daillon.
He was wounded during an exchange of gunfire while being apprehended by police and was taken to a hospital, where he was in intensive care.
Officials said the shooter, whom police did not identify, had spent time in a psychiatric hospital in 2005 and was known to police as a drug user.
Police had previously confiscated weapons from the 33-year-old when he was placed in a psychiatric ward.
Police said he used two weapons in the Valais shooting spree: a historic Swiss military rifle known as a mousqueton and a shotgun.
French police are still investigating the murder last year of a British-Iraqi family in the French Alps, on the other side of the border from the Swiss canton.
Saad al-Hilli, his wife Iqbal and her mother Suhaila al-Allaf, were all found dead inside their estate car near Lake Annecy in Haute-Savoie on September 5, along with a French cyclist who police believe was an innocent bystander.
The couple's two young daughters survived the attack.
Investigators have so far failed to report any progress in solving the case, but have previously raised the possibility of someone with psychiatric problems being behind the shooting.
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The French shootings took place in the town of Chevaline, about 150 kilometres (90 miles) from Daillon.
Some reports have also suggested the weapon used in the French shooting was a Luger P06, a handgun used by the Swiss army in the 1930s.
Swiss media have quoted former friends of the Daillon shooter as saying he was obsessed with joining the military and that his personality had changed after he was rejected.