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Flammable liquid which was stored in a water bottle was poured through the letter box at the front of the building, followed by lit fire lighter blocks which started a blaze.
The water bottle was also pushed through the letter box, in an apparent attempt to dispose of it.
Fortunately, the fire did not take hold and there was minimal damage caused to the building.
It is believed the incident occurred sometime between 5pm on Friday 11 March 2011 and 7am on Monday 14 March 2011.
Officers are now appealing for any witnesses to the incident to come forward.
PC Lewis McLauchlan, of York police, said: “Luckily the post box was closed from the inside, which killed the fire quickly.
“However, this could have been a much more serious incident, with the building being set on fire if the post box had been open.
“I am appealing for anyone who saw anyone acting suspiciously in the area around the time of the incident to contact the police or Crimestoppers as soon as possible.”
Anyone with information that could help the police with their enquiries is urged to contact PC Lewis McLauchlan, of York police, on 0845 60 60 24 7, quoting reference number 12110040567.
Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111.