Fences surrounding fields on the Glebe Road in Carnmoney have been damaged, leading to the death of several cows.
A number of these fields are privately owned and form part of Carnmoney Hill, say police.
Other parts of Carnmoney Hill are a public place, owned by Woodland Trust. As a result of the damage caused, a number of cattle strayed into an adjacent field.
It is suspected that one of the cattle ate fertiliser from the field and died as a result.
Police are appealing for witnesses to the criminal damage.
