im kind of lucky here, my neighbors know that i deal with a lot of rare breeds and show breeds. they keep their dogs home, if i see one here i will usually catch it and call them. but they also know that if it starts attacking any of my chickens, i will shoot it. they would rather me shoot the dog than send them a bill for the damages a dog can do in just a few minutes here.
the last case i had that went kind of rough here, an american bulldog of my neighbors attacked a pen of rhodebars, and a pen of blue slate turkeys. all in all the dog killed about $450.00 in turkeys and 28 rhodebars (at the time their value was higher, maybe $50 each). i had warned these neighbors before, so i shot the dog. i called the sheriff, and asked for them to send a deputy out. the neighbor realized their dog was missing about the time the deputy got here. when he told them i shot their dog, the insisted that i owed $500 for the dog. he informed them that there is a leash law in Ohio, and if i owed the for the dog, then they owed me for the chickens, turkeys and pen damages. they backed down really quick.
this was one of the few times the law worked for me LOL.