sorry to say it mate but if your neighbour finds out and complains and they can prove it was your dog (thats the important thing its got to be proved) then yes your in the shit buddy there is a few acts they'll get you on "stray dogs act " i know your dogs not a stray but it is illeagal not to be in control of your dog ar any time ..... they might also try the dangerous dog act depending on the type of dog depends if its on the dangerous dog list however if it killed a cat they will try that 1 ... remember its has to be proved it was your dog ...if you live in a council house they may also say