Accepted Answer

Since the top has broken off it is his responsibility.

"WHEN A TREE’S GOT YOUR SANITY HANGING FROM A LIMB…HERE ARE YOUR RIGHTS:
If the branches of a neighbor’s tree hang over your yard, you have the right to trim the branches up to the property line. But you may not go to the neighbor’s property or destroy or deliberately harm the tree itself. If you do that, you may be liable to the owner for two to three times the amount of actual monetary loss.
You are responsible for a tree whose trunk stands in your hard. Even though most of a tree may hang into your neighbor’s yard, that tree is still yours. If the trunk stands partly on both your land, it belongs to both property owners.
If your neighbor kills your tree by any means, you’re entitled to compensation.
If you’re worried your neighbor’s tree may fall on your house, you can trim the branches to your property line…but that’s about it. Otherwise, you’ll need to talk to your neighbor. There are two ways out: the city may determine the tree is hazardous and demand your neighbor remove it. Or, if the tree threatens a utility company’s equipment, they may come and trim it."
See: http://www.knx1070.com/pages/41023.php

What this rule is alluding to is that there has to be a balance between competing property rights, yours and the neighbor's. These are the kins of cases that courts struggle with, and have to come up with a Solomon-esque rule which gives guidance to future parties.Here is a statement of the rule from a legal perspective by Attorney Paul H. Nessler, Jr., P.A, which discusses the issues:
"The right of self-help:
"A property owner may cut back branches and roots that stray onto the property owner's property. The right of self-help, as it is called, is not found in state law; however, it derives from the common law. The rationale behind the right of self-help is that, to the extent possible, property owners should be able to protect their interests without the necessity of resorting to the courts.
"Is the right of self-help without limitations?
"The right of self-help is not without limitations. A property owner who engages in the self-help remedy of trimming back encroaching branches or roots must:
- not trim beyond the boundary line of the property owner's property and
- take care not to injure the tree by trimming
And, to the extent the property owner needs to enter onto the property of another in order to complete the trimming, the property owner must obtain permission to do so.
"First Things First
As an initial matter, a property owner troubled by an encroaching tree should consider talking to the owner of the tree. It may be that the parties can agree to split the cost of a professional tree service or work on the trimming together. In that way, each party can take an affirmative role in remedying the problem."
See: http://www.paulhnesslerjrlaw.com/article.jsp?practArea=31&articleIndex=2

thanks for using just answer. An accept for my time is always appreciated

Expert:	Wayne Patterson
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Answered:	11/5/2009

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Experienced in Construction Law and Traffic Law