Nighthawkers are believed to be behind a series of divot holes left in Terrington St Clement Memorial field.
Terrington St Clement Parish Council believes the holes were dug by a metal detectorist when the equipment sounded.
The incidents occurred in the early hours of February 22, overnight on February 11 and January 24.
The field is not believed to have any historical significance and the holes have been repaired.
Police are appealing for information into the incident.