Legal Question in Real Estate Law in North Carolina

Generally speaking, your neighbor is liable only if he was "negligent." In this context, that normally means that your neighbor was on notice that the tree was likely to fall, which typically means that the tree was dead, or otherwise showed signs that it was likely to fall. If your neighbor has insurance, then you can submit a claim and see how they respond. You of course might want to consult with an attorney and provide him or her with more facts.