The "King and Queen", a bronze of a man and woman sitting on a bench, was found at the weekend with both figures beheaded.
The sculpture is one of five Moore bronzes haphazardly laid out in a Scottish country estate near the town of Dumfries. Its owner, entrepreneur Tony Keswick who started his collection in the 1950s, was away on business.
Detectives said Monday it was probably vandalism but did not rule out political activists as the culprits.
Police Inspector John Houston said: "We are still looking for the heads and we'll know more when we find them."
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