Does your town/city have any provisions nowhere they can force removals? Many don't, but some do. If so, find out what that process is. And document it. If they determine it doesn't meet their threshold, ask for that in writing and send a copy to your insurance. (Insurance will go after them too if the tree does fail...)This is a battle right now I am having with my neighbor. My insurance stated neighboring trees needs to be removed or there will be no chance of insurance coverage. I have talked to him but nothing has happepened yet. I am not waiting just planning on filing suit and punitive damages ASAP. Thanks
If that isn't an option, have a TRAQ arborist evaluate the tree (from your property - unless you have permission). Get a written report. Have an attorney send (or maybe you Ins Co will?) a letter requesting removal for safety reasons based on the risk level of the report. Or send a copy of the report to insurance of it is deemed a "low risk" tree.