Putting your unfortunate and understandably expensive lawsuit aside... If its a 10 year old tree and the building cannot afford to maintain it, which involves cleaning the pit, occasionally pruning it and sweeping he leaves in the fall; I don't mean to sound harsh, but the building may have more significant problems than the tree itself.
On the flip side.. If the tree were damaged by an accident or unintentional issue, or diseased, or dead from, say some kid driving a nail into it or something, you would be permitted to remove it. .. I wouldn't condone doing anything, but that's just something I heard...