Nope (though it does depend). I’ve been through several trees falling from storms.

Unless negligence is involve (like an arborist being hired to condemn a tree), they’re generally considered and act of god. They’re the responsibility of the property they fall onto.

So, in the case of OP, the situation is unfortunate, but it’s on him to maintain his properties and his fence lines within his properties. It’s convenient the state has a fence along part of his property, but it’s not their responsibility to fix it for adjacent lots.