I have found the city to be very helpful.

For more information on sidewalks, check out the city's Sidewalk and Parkstrips web page: http://www.sanjoseca.gov/transportation/s_sidewalks.htm

In regards to trees located on the park strip is a city tree, the home owner is still responsible for its care. However, the home owner needs a tree trimming permit to prune the tree, the permit is good for up to 60 days (up to a 30 day extension) and the upkeep is subject to inspection upon completion.

More information can be found at http://www.sanjoseca.gov/transportation/tl_treemaintenance.htm.

I hope that helps!