Legal Question in Personal Injury in Washington

Yes, it is possible to be sued under the circumstances you present. For example, if the tree was rotten and dying or severely slumped over, the law will often hold that the owner has a duty to ensure the tree is not in danger of falling onto a neighbor's property (as one example). This type of situation often comes down to whether the owner knew about the trees condition, or should have known about it, and if they knew or should have known and did nothing, then they have breached their duty to the person harmed to do something to avoid the risk the tree poses.

It can get very complicated and these are often very fact specific situations, which I can't go into given that you have provided very little in the way of facts. That said, I think this takes response goes as far as I can with what you've provided.