The union said the fire started in a bathroom of the office at about 5 a.m. Tuesday. No one was in the building and the fire was doused by a sprinkler system.
Union spokesman George Atallah said there was more water damage than fire damage. There was some concern of damage to items belonging to the late Gene Upshaw, Smith's predecessor as executive director.
Atallah said the union and Washington fire department are investigating.