Check with your local government to find out whether there are any laws restricting where you can work or how much material may be left behind after a tree has been removed (e.g., in parks). Naturally, you cannot simply trim or cut a tree, regardless of its health status without proper licensing requirements.
Trees are vital part of our ecosystem. Whenever a tree is fallen, they must be replace for the furture genertaion. However, there are old trees that may need to be cut since they are causing hazards already. In this case, you need to know the government regulartions regarding tree felling. Or better yet, seek the help of a professional Wellington Arborist for more assistance.