An 80-foot maple tree located on our neighbor's property (wooded hill-side) close to our property line and right behind our house posed an imminent danger to our house and life in case of a storm. During Sandy three trees on this property were uprooted and feel on our neighbor's house. We were concerned about the safety of this tree and had an evaluation done by an arborist. The evaluation confirms the imminent danger of this tree, particularly after the stresses of Sandy. Since the owners of our neighboring house live overseas, we contacted the tenant about this situation and informed her that we plan to cut the tree down. We discussed the fact that we would like to split the cost with the owners and asked for information on how to reach them. The tenant gave us the agent's phone number. The tree was cut and we contacted the agent to discuss the possibility of splitting the cost. Agent informed us that the neighbor wants to file a lawsuit for trespassing. What are our rights?

I'm in NY - you could ge sued for the value of the tree. It does appear that you trespassed if you entered their property and cut the tree without permission.

You asked for permission but then cut the tree before you got it? Or something else?

Bottom line - maybe the arborist will testify that the tree was an immediate danger. Maybe not.

Either way, you trespassed.

Trespass is a criminal charge, by the way. You would be arrested for trespassing and sued for cutting down a tree worth X dollars.

Agent informed us that the neighbor wants to file a lawsuit for trespassing.

If the neighbor you refer to above the owner or the current tenant? Did you state that on x date you would be entering the property and removing the tree? Did you do this before contacting the owner?

If it's the tenant and you informed them that you were cutting the tree down and they did not object then they can't complain. But if you cut the tree without getting the owner's permission, then they can file criminal trespass charges AND sue you for the value of the tree.

It is unlikely that a local prosecutor would prosecute you and hopefully the arborist can testify that the tree was a danger so that a judge will not award the owners damages.

... The tenant gave us the agent's phone number. The tree was cut and we contacted the agent...

Why, pray tell, did you go to the trouble to get the agent's phone number and then wait until after you cut the tree to contact the agent? Were you intentionally trying to do it arse-backwards?

Backwards indeed. If I were the owner, you might have had a chance of me splitting the cost, but not when you merely 'informed my tenant' of your plan to cut it down without permission. I'd sue you for whatever I could just on principle.

I will be astonished if the arborist testifies on behalf of the OP - astonished. No licensed arborist is going to get into this scenario.

I get called into "tree" situations on a fairly regular basis. This is not foreign to me.

An arborist saying a tree is a danger is NOT the same as that same arborist giving the homeowner a letter stating that the neighbor's tree is an imminent danger to the client's property.

I think OP moved too quickly - for whatever reason.