J.R.
There are leash laws most everywhere. I do not know of any town in my area that does not have one. There are also laws about picking up dog poop while on walks etc. You can actually be fined if you are walking your dog without a baggie...
When we moved into our new home, the very first home improvement we did was a fence. Evidently my neighbor's kids thought our yard was free game for their football games. All fine and good... I try not to be a jerk about these things, but they were ripping up our lawn. Now evidently they don't care at all about their lawn because it's about 40% ripped up, and what grass they DO have is about 9 inches high... if they don't mow this weekend, I will be calling the village. (did I mention the huge brown spot of dead grass where their broken trampoline sat for 5 months upside down? And the numerous coolers and a disassembled tent that is still out back from a party they had at the beginning of LAST summer? and that I am now spending about 8 grand to have privacy landscaping put up so I don't have to look at the eyesore they call a yard? UGH!!!)
They also HAD a dog, don't know where it is now... but after school the PIT BULL chased my kids into the garage... all the way up the stairs of the garage. I admit... I had it at that point and all possibility of being a 'nice neighbor' went out the window. I went outside and said the next time I see this dog loose I am locking it in my garage and calling animal control... you want to keep it, keep him leashed!
You may want to call the village about the dog laws in your town... tell them about what you are dealing with with your neighbors dog and then go over to the neighbor and say look... there are laws that need to be followed if you own a dog, and I don't want to call the police or go that route... please keep your dog out of my yard, or I will have to bring them into this.
Good luck!