Real Estate Law
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If the tree's roots are damaging the house and you can get an arborist to state this i na report, then you can sue the neighbor for "private nuisance" and force them to abate the nuisance. A private nuisance is an interference with a person's enjoyment and use of his land. The law recognizes that landowners, or those in rightful possession of land, have the right to the unimpaired condition of the property and to reasonable comfort and convenience in its occupation.
If the roots have caused damages to the foundation or other areas, the you can also sue them for the cost of any repairs. Any time the roots of their tree enter your property, that is a trespass to your land by their personal property (i.e. the tree). So you can hold them liable for any damages that their tree causes you.
As part of the suit, you can either seek an injunction to force the neighbor to remove the tree, or to compensate you for the cost of cutting any roots and for any damages that they have caused.