In missouri, my neighbors tree limb are sagging over into my patio, whos pays for the removal?
You do.
I agree that an arborist should do the work, but if a neighbor's tree limb overhangs your property you own the right to prune it (which means you have to settle up for it) . However you have the obligation to do the work using currently agreed pruning techniques so as to minimize the harm done to the tree. I might donate.
that in certain states, trees are protected property and neighbors don't other have the right to trim up a tree. I agree that you should talk to your neighbor since doing anything...if his trees are valuable, he might wish to hold them pruned by an arborist rather than a neighbor with a chainsaw since unbecoming pruning can cause a tree to become diseased.
Answers: Probably you do. You should talk to your neighbor first - tell them the limb are too shady, too messy, too hazardous to your garage, whatever reason you want them removed. Ask your neighbor if he is going to be reluctant if you have them cut. He might want it trimmed up on his side too, and you can split the cost fairly.
If the tree falls on your side of the barricade, it is the responsibility of your insurance, not his. Your insurance company might go after him, but his homeowner's isn't going to cover it.