The blaze broke out at 4am on Friday September 20 at the JobCentre Plus in Bank Street, Alexandria, West Dunbartonshire.
Police said that windows of the building were smashed and that an attempt was made to set fire to the interior of the premises.
The man seen in the footage has his head covered with a plastic bag and is wearing a light coloured camouflage jacket, with a black leather jacket underneath and light coloured trousers.
He had a man's mountain bike with a white basket on the front.
Call police on 101 with any information.