This is another common real property question. There is a reported case decision that say you may cut or trim any part of that tree which extends over your property line. Of course, working in tandem with your neighbor may promote a better relationship, but you can take unilateral steps to protect your own property. But any action on his side of the line would require permission, or even a court order that he abate a nuisance.
If the tree is overhanging your yard you have the right to cut it back to the property line. You cannot cut it back so severely, however, that your cutting causes it to die.
This answer does not create an attorney client relationship