If entire trunk is on one side of the property line, the entire tree belongs to the owner of that property and adjoining property owner MAY NOT CUT any branches, roots or harvest any fruits or nuts without the owner's permission.
The tree belongs to both of adjoining landowners. In this case, neither can destroy the tree without the consent of the other. Either landowner can cut his/her property if in so doing he/she doesn't destroy or permanent damage the tree.
From Horticultural Science 13(4):634