Although Burbank is an unincorporated area (a "County Pocket" or "Urban Island"), and is not a part of the City of San Jose, you may find some of the information on the City's Services web page useful. There are links to the County Sheriff, Fire Department, and other services used by Burbank residents. There is also a 24/7 phone number that you may find useful.
The information in these links will be most useful to residents of areas adjacent to Burbank that are actually part of incorporated San Jose.
San Jose City Services
The Neighborhood Trouble-Shooter is a handy reference guide designed to identify San Jose City and community resources that can assist you in answering questions and solving problems.
Neighborhood TroubleShooter Guide