You can not sue him or restrain him from doing something that has not happened, and "may" occur at a future date. You can trim any part of the tree that encroaches into your property. But you can not make him pay for it.
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I'm really sorry that you have to deal with such a person. My colleague is correct -- you can't take legal action for something that has not yet happened. In attempting to be creative here, and this suggestion is what I would consider a stretch, but maybe your local zoning ordinance prohibits the planting of trees within a certain setback area from your property line. Many zoning ordinances have setback provisions -- which require structures not to be placed in setbacks -- and I have on occasion seen setbacks regarding trees. If your zoning ordinance has such a provision, you might be able to call code enforcement on your neighbor and force the removal of the tree.
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