Two sheep have died and four more have been injured following a dog worrying incident in Sutton Parva, near to Warminster.
The incident took place at Haydon Farm between 9.30am and midday on Saturday January 16.
Two sheep later died and four suffered "serious bites", say police.
Officers are now appealing for anyone with information to come forward.
PCSO Candida Jackson said: “Dog owners are reminded to keep their animals on a lead in the countryside, a dog that normally runs around the local park is faced with a very different environment when they are walked in the countryside and may encounter farm animals for the first time.”
The sheep were in a field next to the 5th Milestone byway which can be accessed from the A350 that runs through to Downlands Church Farm, Tyrtherington.
When sheep are worried by dogs, it can cause extreme stress to the animals.
Sheep can bunch together, crushing each other and this can cause shock which can be fatal, or cause them to abort their lambs.
Sheep worrying and dog attacks on sheep are crimes and can result in large vet bills for the farmer and dog owners may be liable for compensation for any damage to the sheep.
Anyone with information about the dog attack should call 101 quoting log number 54210005206
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