Police are not taking any further action after two sheep drowned.
The animals, which belonged to Dunstan Square Farm, were chased into the sea at Craster by a dog that was not on its lead, despite warning signs.
It is believed that the dog belonged to a holiday-maker visiting the area.
Last week farmer Ali Grey, who owns the farm, urged dog owners to keep their pets on leads, especially at this time of year when ewes are getting ready to lamb.
Meanwhile, the British Veterinary Association has put out a warning to dog owners.
President and vet Robin Hargreaves said: “Over the coming months ewes in the field are likely to be heavily pregnant or to have recently given birth.
“Chasing and worrying can have severe consequences at this time, leading to serious injuries, early labour and fatalities.”