The attempt generally failed because gasoline splashed inside some offices and a hallway did not ignite. Damage was minimal.
Court proceedings went on in the building Wednesday, but the offices were closed at noon and it was unclear if they would reopen on Thursday.
Treasure County Attorney Gary Ryder said an arsonist broke a window at the rear of the courthouse Tuesday night or early Wednesday and then poured gasoline inside the judge's chambers, the justice of the peace office, Ryder's office and in a hallway.
Ryder said some clothing in the judge's office burned but the fire failed to ignite the hallway gasoline trail or trigger other fires.
Deputy State Fire Marshall Jerry Smith of Miles City was investigating, along with personnel from the Department of Justice in Helena.
There was no estimate of damage.