The sheep were among 24 livestock animals believed to have been attacked by an unknown dog.
Five others required stitches and a further 14 were prescribed a course of antibiotics for their injuries.
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The incident happened on Monday, April 22 in a field in Farthinghoe, near Brackley between 10.30am and 4.30pm
Rural Crime Sergeant Abigail Anstead, who is investigating this incident, is reminding owners that they have a responsibility to keep their pets under control, and that dogs chasing livestock can legally be shot dead by farmers.
She said: “Whether farmer or pet owner, the death of an animal is devastating, but all of this is completely avoidable if people walking dogs keep them on a lead and under control around farm animals.
“This simple measure is part of responsible dog ownership, helps to protect pets and livestock alike, and means everyone can enjoy our beautiful countryside both safely and responsibly.”
Witnesses or anyone with information which could assist the investigation are asked to call Northamptonshire Police on 101 or alternatively, call Crimestoppers anonymously on 0800 555 111.
Please quote incident number 24000176610 when providing any information to make sure it gets to the right person as quickly as possible.
Police have also reminded owners they have a responsibility to keep their pets under control, and that dogs chasing livestock can legally be shot dead by farmers.
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Anyone who shoots a dog to prevent livestock worrying must notify the police within 48 hours.
Earlier this year, police urged dog walkers in the county to use a lead around fields with livestock due to numerous incidents of sheep being injured.
In conjunction with the National Sheep Association (NSA), Thames Valley Police placed signs around dog-walking areas which contain livestock to warn people.
Releasing a statement online, police said: “Last year we had numerous incidents of dogs worrying sheep, and injuring them.
“Thankfully these incidents, whilst rare, do however have an impact on the animals and can negatively affect pregnant sheep and lambs especially.
“As a general rule if you and your dog pass through a field with livestock in, please use a lead on your dog, it is not enough to expect perfect recall.”
Incidents of livestock worrying should be reported online to the police or by calling the non-emergency 101 number. If the dog is in the process of worrying livestock and cannot be stopped, please call 999.
