Hello Leticia,
You should start by calling your city’s administrative office to find out if the sidewalk is your responsibility. This varies significantly from city to city. Some municipalities consider the sidewalk to be your responsibility to maintain. In others, it could be a a 50/50 split where you pay half of the repairs. In my city they consider the sidewalk and the “beauty strip” of grass between the sidewalk and road to be a utility easement that they own and control.
I agree, you should call your local jurisdiction. Here in Florida IF it is deemed your responsibility, you would hire either a Residential, Building, or General Contractor to perform this service. The sidewalk and the apron of your driveway are considered Common space and are usually County or City property and are typically 6" thick. For that reason they prohibit a Specialty Structure Contractor from performing such services. This will also require a permit, without one you may get a Red Tag which comes with a 4x’s the permit cost fine and be required to remove the concrete.
As of recently, we have had quite a few homeowners that have received notices stating that they have 30 days to fix “their” sidewalk due to tripping hazards. Now, that is here in Pittsburgh, PA. It is the homeowners responsibility, but when trees are involved (roots lifting and cracking the sidewalk), those belong to the city… so we have had to call out the forestry department, have them take care of the trees, and then fix the sidewalk at the owners expense. Hope this helped… Thanks! 
