Clarification/Follow-up by Jim.McGinness on 09/12/06 1:27 pm:
First guess is that the owner is responsible. There may be circumstances, however, that limit what you can do with the tree or that make someone else responsible for certain kinds of maintenance.

If you tell us where you live and where the tree is located in your yard someone may be able to give you a more specific information. Is the tree possibly located in an easement?