As soon as possible! If you suspect a tree is dead, call an arborist to evaluate its risk and then make arrangements to have it removed immediately if it poses the possibility of striking a home, car, or passers-by. If the tree is in no danger of striking anything if it falls then you would be safe to remove it within a reasonable time, approximately six months. It is important to remove dead trees because if the tree died from a spreadable disease, then you want to remove that diseased tree before the infection can find a new host in nearby trees.