Four sheep were killed after being attacked at a farm in Offham.
Between 3pm on 3 December and noon on December 5 a flock of sheep were attacked by a dog or dogs at Mill Laine Farm, Offham.
A further 18 sheep suffered serious injuries to their faces, tails and legs.
PC Garreth Evans said: “We are appealing for witnesses or anyone with information to contact us.
“The dog or dogs involved would have been exhausted after such a prolonged attack and would have been covered in blood.
“I would urge owners to keep their dogs on leads around farming fields and ensure they have control of them at all times.”
Anyone who has information about the attack is asked to contact police on 101, email firstname.lastname@example.org quoting serial 0279 8/12 or the independent charity Crimestoppers on 0800 555 111.”