Washington law states that if you enter another's property unlawfully and cut, damage, or remove any tree, shrub, or plant material, you are liable for triple damages + attorney fees. However, if you stay on your property and do the same thing, you're only liable for actual damages (1/2 a tree).
Your options are:
1) Get the neighbor to agree that you may cut down the tree.
2) Cut it down and hope the neighbor doesn't sue you.
3) Cut off any part of the tree that extends over your property line (branches, protions of trunk, roots, etc.). These parts of the tree belong to you and you can do whatever you want with them. This will of course kill the tree, forcing the neighbor to take the rest of it down. Expect your neighbor never ot talk to you again.
4) Build your fence inside or around the tree.
5) Build your fence right up to the tree trunk. An aerial view would look like this: ----0----
In all cases, get a survey of your back property line. You may find the tree is entirely yours. Lots of fences in Washington are 2-6 feet off the line, due to the limitations of survey techniques decades ago.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.
[This message has been edited by Tracey (edited April 28, 2000).]