In Auburn, the city's Building Services division issues building permits for construction, additions and alterations, and the city says many activities, construction among them, need a permit. Whether your steps need one isn't something I'd guess at, so I check it for your address before we schedule, and we handle the application when the job needs one. If you'd like to ask yourself, the city's Permit Center takes calls at 253-931-3090, option 2.
The first thing to settle is which office's rules apply, because some properties with an Auburn address actually fall under King County, Kent or Federal Way. The city's interactive map, linked from Auburn's permits page, shows whether a property is inside city limits. Work in the public right-of-way, the public strip along the street, needs its own construction permits, and the city requires a licensed and bonded contractor for it.
We're based in Auburn and work in the cities around it, including Kent and Federal Way, so an address near a city line doesn't change who builds your steps. Most of the step calls we get around here are for front entries where the old concrete has cracked, chipped at the edges or settled away from the door.