Several police units were sent to the village of Vikene after people reported hearing shots at 5.30pm.
“Everything seems to suggest that it was a murder and a suicide,” said police spokesman Tord Carlsson.
Police were reluctant to reveal details about the victims, other than that the bodies were those of a man and a woman.
“They are lying about 100 metres apart from one another,” said Tord Carlsson.
Police have sealed off the area around the apartment block where the incident took place.