Trees can, at times, be planted and grow very close to a property line. If the tree is ever located inside of the property (but is not touching the property line) it is a private tree. If the tree is on the City portion of the property, it is the City's responsibility to maintain it.
If you are uncertain if a tree is privately or municipally owned, you may submit a request to have a Forestry inspector determine the ownership of a tree.(link is external)