Yeah it's in the article:

The weapon used in the shooting was a registered handgun that was licensed to the suspect’s relative, Detective Inspector Kimmo Hyvärinen said.

Also seems like they are relatively lax with guns:

In the Nordic nation of 5.6 million, there are more than 1.5 million licensed firearms and about 430,000 license holders, according to the Finnish Interior Ministry. Hunting and gun-ownership have long traditions in the sparsely-populated northern European country.

Responsibility for granting permits for ordinary firearms rests with local police departments.