In certain circumstances, killing a dog is legally justified, and a person who does it isn't financially liable to the dog's owner. For example, if someone kills a dog because it is threatening to injure a person or livestock, the action is justified by law.
Generally, it's perfectly legal to do anything necessary to stop a dog caught in the act of attacking a person or livestock. A dog's owner is not legally entitled to any money from someone who injures or kills the dog while protecting a person or farm animal from attack. Nor is the person guilty of a criminal offense; many animal cruelty laws specifically exempt the act of injuring or killing a dog in these circumstances.
"Livestock" usually means only commercially valuable animals, not pets or wild animals. Some state laws list the kinds of animals protected; others say only that a dog may be killed if it attacks a "domestic animal," which historically does not include dogs and cats. Dogs and cats may even be specifically excluded; for example, in Ohio it's legal to kill a dog that is chasing or injuring a "sheep, lamb, goat, kid, domestic fowl or domestic animal except a cat or another dog." (Ohio Rev. Code § 955.28.) Someone who does injure a dog that's chasing another dog, or a deer, may be liable for damages to the dog's owner—and the killer may also be guilty of cruelty to animals.
A farmer or rancher doesn't have to wait until a dog has sunk its teeth into a calf or lamb; most laws allow killing a dog that is chasing or preparing to attack livestock, or fleeing after an attack. In Kentucky, for example, any dog that is "pursuing or wounding any livestock" can be killed. (Ky. Rev. Stat. § 258.235.) The dog must, however, be caught in the act. As one court put it, "it is not the dog's predatory habits, nor his past transgressions, nor his reputation, however bad, but the doctrine of self-defense, whether of person or property, that gives the right to kill." (State v. Smith, 156 N.C. 628, 72 S.E. 321 (1911).)
Hunting down a dog after an attack has taken place is not allowed. Generally, a farmer may legally kill a dog only on the farmer's own property. An Illinois court ruled that a sheep farmer who followed a dog back to its owner's home (in a residential area, no less) and shot it there an hour after the dog had killed some of his sheep was not protected under the Illinois statute. (People v. Pope, 383 N.E.2d 278 (1978).) Instead, he should have sued the dog's owner for the value of the sheep killed. (In many places, farmers or ranchers who lose livestock to dogs can also apply for reimbursement from a county or state fund.)
A dog is not, however, necessarily safe as soon as it leaves the farmer's property. In general, a farmer who wants retaliation is allowed to pursue a dog for a "reasonable time." What is a reasonable time under the circumstances is a question that's resolved when the lawsuit gets to court.
For example, a Kansas jury vindicated a farmer who shot and wounded a dog he found attacking his hogs. He shot at the dog, but it ran away, with the farmer in hot pursuit in his pickup. The dog ran home, where the farmer shot it twice and left it hiding, wounded, under the house. When the dog's owner came home, he rushed the dog to a veterinarian; it eventually recovered. The owner sued for almost $8,000, but the jury came back with a verdict for the farmer. (McDonald v. Bauman, 433 P.2d 437 (1967).) The Kansas statute allows a livestock owner to kill a dog that has been found injuring livestock "a reasonable time" before.
A farmer must also produce proof that the dog was chasing his livestock. In an old California case, for example, a rancher's belief that his sheep were in danger from dogs was not enough, the court ruled, to absolve him of financial responsibility for shooting them. (Johnson v. McConnell, 80 Cal. 545 (1889).) Testimony indicated that the dogs were following a herd of pregnant ewes, which were agitated and frightened. The dogs' owner successfully sued for $225 (this was in 1889) for the injuries to his three highly trained dogs.
Most statutes do not allow a farmer to shoot dogs that are merely running loose (at large). A North Dakota rancher, who shot a neighbor's greyhound after it ran through his cattle herd without particularly disturbing the cattle, was not protected by the state statute, which allows killing a dog only if it is "worrying" livestock. The rancher had to pay $300 to the dog's owner. (Trautman v. Day, 273 N.W.2d 712 (N.D. 1979).
Some states, however, allow farmers to shoot any dog that is, in the words of the Indiana statute, "roaming over the country unattended." Under this statute, an appeals court upheld the right of a farmer to shoot dogs he said were trying to get into his chicken pen in the middle of the night. (Puckett v. Miller, 381 N.E.2d 1087 (Ind. App. 1978).) The dogs, two coonhounds, had been hunting with their owner but got separated from him in a heavy rainstorm about 2 a.m. (For the uninitiated, raccoon hunting is done at night.) Under the relatively severe Indiana law, it made no difference that the dogs were bothering the chickens; their hours were numbered as soon as they got away from their master.
If you lose a dog to a trigger-happy farmer, in most instances, there is absolutely no way to prove that it wasn't doing what the farmer or rancher who shot it says it was doing. The only other witness is likely to be the dog, and it isn't talking. So the lesson is simple: If you live in a rural area or close to one, NEVER let your dog run loose off your property. Farmers may shoot first and ask questions later, if at all.