Legal position on dog killing/injuring a cat

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We have moved house and there seem to be a lot of cats around here. I have a greyhound who is most definitely not cat friendly. He is always muzzled when out on walks. Our garden is secure and when the weather is nice like today I would like to be able to open the patio doors so my dog and children can come and go freely.

If a cat should enter my garden and be injured or even killed by my dog where would we stand legally? It seems unfair to keep him muzzled in his own house on the off chance that one should be foolish enough to come into the garden. On the other hand apart from the awfulness of having a cat be injured or killed I do not want to risk that something happens and then find out that we could be prosecuted or my dog ordered to be put down. I've read conflicting things online.

And the point /my point being Jon is that it isn’t an offence.

I did read it properly. Thank you.

Your dog would not be euthanised if it were to kill a cat OP.

I agree that it is an offence. The exemption under s3 (1A) applies here the dog is in a domestic building. In this instance OP is asking about what happens if the dog is in the garden.

Also agree that it is an offence if a dog is dangerously out of control anywhere other than in a domestic building.

DLO here- nothing will happen. Your dog will not be euthanized. If anything, it would be a civil matter but will get thrown out pretty quick.

Not many dogs get put down for killing other dogs/injuring people so a cat that has entered your garden, is not going to be an automatic destruction order.

^^ Assuming you are in the UK of course.