The two men are said to have checked in at a smaller hotel in Östersund on Tuesday.
However, the names they provided at check-in were never checked against ID documents, according to the police.
On Thursday, hotel staff discovered that parts of the interior had disappeared.
Where the men lived, two double beds, two TVs and a vacuum cleaner were missing.
The bill was also left unpaid at the hotel.
If anyone has seen two people carrying bulky furniture at odd times along the main street in Östersund, the police are grateful for tips.
They can be reached on telephone number 114 14.