Petrol soaked rags were pushed through a letterbox of a flat in Fife before being set alight.
Police are hunting the man responsible for the fire-raising attack in Links Street, Kirkcaldy, between 04:30 and 05:30 last Friday.
The owner of the flat was able to put out the fire before the emergency services arrived.
Officers are urging anyone who was in the area at the time, or has information to contact them.
Det Insp Paul Dick, of Police Scotland, said: "This fire was a deliberate act and we are following a number of inquires and are also carrying out door to door inquiries in the area.
"I would be grateful if anyone who was in the area between 04:30 and 05:30 and who hasn't already spoken to the police to contact us."