This situation annoys me, probably as much as it annoys you.
* YOU don't have a dog or a fenced in yard for it to play in. Your couldn't care-less neighbor has both, yet takes no precautions to protect his dog by keeping it in his own yard or keeping it on a leash. There are LEASH laws in darn near every city--look up yours online on your city's page. Usually 4-6 ft is the farthest away from you that a dog can be when it's off your property.
* Now you're worried about this bozo suing you if his dog DOES die, when in fact he could easily just induce vomiting (hydrogen peroxide in the correct dose for his pet) or heck take the dog to the emergency ER for a checkup.
* YOU are not at fault here in any way. If things go wrong, the law is on your side.
* BUT keep a camera/cell phone handy (preferably the kind that puts the date and time right on the photo) near the windows where you most often see the dog running loose. Then you'll have more evidence of neglect and animal cruelty on the part of the poor dog's idiot owner.
* Be sure to call the dog catcher every time you see the dog running loose, too. Maybe if enough people complain, they will take the dog away from it's poor-excuse-for-an-owner and find a really nice "forever" home for it where people do care enough to keep their dog on their property, off the streets, off other peoples' property, etc.
* This calling the dog catcher thing is starting to work in my neighborhood of German Shepherd Dogs, Akitas, and Labs that would be big enough to gobble me and my Lab up in one swallow! (We drive to other neighborhoods to walk and exercise--our house is right by two major freeways!)
With no negative consequences, this moron will end up continuing on the same path until one day it kills the dog. So very sad and frustrating! I sure sympathize, peeples, with your problem. Very good luck!!