What are my rights and responsibilities regarding a boundry tree? My neighbor wants to cut it down and have me pay half the bill

Question, who planted the tree? - also is the tree an actual nuisance - does it show signs of falling imminently?

I agree; if it's a liver oak, chip in together and hire a licensed arborist and split the cost - this would your best shot at a workable compromise. Any other resilt will cost FAR more than that to achieve. Hope this helps. gsg

Can't say for sure. It sounds like it started on your neighbor's side of the property and now partially covers the boundary. best suggestion is to consult with a real estate attorney in your area to determine the best course of action. Sortof depends upon the location of the tree and how it is leaning.