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The statue may be subject to copyright, depending upon its age. The owners of the property upon which it sits - both the cemetery and the plot - and the family that owns the statue itself may raise moral, ethical or legal objections.
Your best bet is to first approach the the guardians - the owners of the cemetery - who will generally be appreciative of your considered approach and help you through the minefield. If that fails, you can always ask the family that owns the plot.