Over £800 of damage was caused to a summerhouse in South Church, near Bishop Auckland, on Monday morning when it was set on fire.
The building, in a garden on Appleby Street, was attacked between 10.30am and 2.45pm.
Anyone with information is asked to call PC Sarah Rooney at Bishop Auckland police station on 0345-60-60-365 or Crimestoppers on 0800-555-111.
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