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 spokesman told AFP.
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 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 5th, 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.