Ohio law: Note-Be sure to Google "Ohio 955.261 Revised Code" and read that as well.
955.28 Dog may be killed for certain acts; owner liable for damages.
(A) Subject to divisions (A)(2) and (3) of section 955.261 of the Revised Code, a dog that is chasing or approaching in a menacing fashion or apparent attitude of attack, that attempts to bite or otherwise endanger, or that kills or injures a person or a dog that chases, threatens, harasses, injures, or kills livestock, poultry, other domestic animal, or other animal, that is the property of another person, except a cat or another dog, can be killed at the time of that chasing, threatening, harassment, approaching, attempt, killing, or injury. If, in attempting to kill such a dog, a person wounds it, the person is not liable to prosecution under the penal laws that punish cruelty to animals. Nothing in this section precludes a law enforcement officer from killing a dog that attacks a police dog as defined in section 2921.321 of the Revised Code.
(B) The owner, keeper, or harborer of a dog is liable in damages for any injury, death, or loss to person or property that is caused by the dog, unless the injury, death, or loss was caused to the person or property of an individual who, at the time, was committing or attempting to commit criminal trespass or another criminal offense other than a minor misdemeanor on the property of the owner, keeper, or harborer, or was committing or attempting to commit a criminal offense other than a minor misdemeanor against any person, or was teasing, tormenting, or abusing the dog on the owner's, keeper's, or harborer's property. Additionally, the owner, keeper, or harborer of a dog is liable in damages for any injury, death, or loss to person or property that is caused by the dog if the injury, death, or loss was caused to the person or property of an individual who, at the time of the injury, death, or loss, was on the property of the owner, keeper, or harborer solely for the purpose of engaging in door-to-door sales or other solicitations regardless of whether the individual was in compliance with any requirement to obtain a permit or license to engage in door-to-door sales or other solicitations established by the political subdivision in which the property of the owner, keeper, or harborer is located, provided that the person was not committing a criminal offense other than a minor misdemeanor or was not teasing, tormenting, or abusing the dog.
CREDIT(S)
(2008 H 71, eff. 9-30-08; 1987 H 352, eff. 7-10-87; 1953 H 1; GC 5838)
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Now, here's how I would approach this. There would most assuredly be a meeting between myself and the neighbors. I would inform them what happened, that another neighbor ID'd their dog as the culprit, and go over all the rest of the facts you have. Calmly, but to the point. Nothing is going to bring those chickens back, you have to start again. There is no point in letting things get heated during the meeting, but there is every reason to be straight and to the point. I would have a copy of this law for them to read and keep, and tell them that you expect them to pay for your loss, which figuring in your time, feed, etc., is more than a few dollars a bird.
Straight, calm, but to the point. I would make sure they understood that the law clearly states that you have the right to kill their dog, if it is even approaching your chickens aggressively, which is what the law says in plain English. I would also tell them that I certainly would hope it doesn't come to that, that neighbors and adults can solve the problems faced in our lives.
You start at the beginning:
"Listen, this is going to be a difficult and stressful conversation for all of us, I wish this was easier to get through, but it's not going to be. I hope the police don't need to be involved. Here is what we need to talk about, your dog killed most of our chickens..." and get through it. If they start getting hot and go in to denial, then you can either stop altogether, or just ask them to hear you out, and you'll answer the questions they will ask after you've said your piece.
If they get all hot and angry and hostile, then I would back off. This would be followed by a written complaint made to the police, and I would do it that way. But don't avoid it, and don't back down either.