Your question covers a pretty common problem that arises between neighbors. In California the owner of a tree is responsible to make sure the tree doesn't cause damage to adjoining neighbors. But the owner is not responsible for the mere fact that the tree encroaches. And in most normal cases the owner wouldn't be responsible for the adjacent owner's time and expense to deal with leaves, pine cones or needles or small branches.
The adjacent owner can prune and trim branches that overhang, but not past the point where it would damage or kill the tree.
The same common sense approach applies to roots. An adjacent owner does not have recourse simply because roots grow into his/her property. That owner may trim or cut the roots but cannot harm or kill the tree in doing so.
But the neighbor may be liable for damage or additional expense caused by invasive roots as in your question. You should considering discussing the matter with the insurance company that handles your homeowner's policy.
Note that my response does not create an attorney-client relationship between us. You should not rely on my response in any way as legal advice. I urge you to talk with an attorney in a timely manner about the specifics of your question before making any decisions.