If the facts are exactly as you state, no, you are not. They are liable to you for damage to your fence, for any injuries to your dog, and any medical bills arising from the bite. If you have not already done so, you should report the incident to animal control.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
My colleague is correct - if the incident happened as you say, it is the neighbor who has liability for damage their dog did. Be sure to report the incident to local authorities.
(THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.)
The prior answers are correct as long as the dog was not invited on your property. If the dog had been there before, you need to make sure that they cannot prove the dog had an open invitation to come on your property.
Your were bitten by your neighbor's dog. It may also be that your dog was bitten by your neighbor's dog. This means the issue of rabies needs to be addressed - immediately. If your neighbors cannot document that their dog is vaccinated, you may be in for a series of expensive, painful shots. Assuming that dogs are required to be licensed in Fresno and that proof of rabies vaccination is required to get a license, the city clerk may be able to prove the dog was vaccinated.
Next step is documenting your damages. That means photographing the hole the dog dug under your fence and your repairs to the fence and/or filling of the hole. It means any medical costs you have incurred for the treatment of your bites and vet bills for the treatment of your dog.
That the attack should be reported to the police and animal control has already been stated.
You can likely file in small claims court for your damages. Should you be sued by your neighbor, your defense is that their dog invaded your yard and attacked your pet. Your counter-claim is for your expenses from their dog's acts.
Should legal assistance be required, your state and county bar associations can assist you with referrals.
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