Dear Staten Island Home Owner:
All the signs you post and all the precautions you take will not prevent someone from suing you if injured on your property. But your insurance agent may suggest fencing the yard as a preventive barrier to the risks you perceive.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
In addition to the correct answers you have already received, I'd like to suggest that you call and repor them if (1) their dogs are running freely and entering your property; or (2) they are trespassing on your property to capture their dog. I'd suggest taking photos of both next time it happens, in case you need to document it in court later. Good luck!
I'm just 3 "helpful" answers away from a free toaster-oven! I may be guessing or not licensed in your state. No atty/client relationship exists.
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