The incident took place between the evenings of Friday March 1 and Saturday March 2 at the shared offices of Kilbrandon House.
Officers are appealing for anyone who saw what happened or anyone with information to come forward.
Constable Dorian Stone, Lochgilphead Police Station, said: “Vandalism and graffiti have no place in our community and are not victimless crimes.
“Someone in the community will know who is responsible for this and I’d urge them to come forward and speak to us.”
Anyone with information should contact Police Scotland on 101 quoting reference 3508 of March 2.
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