Is it possible to get the municipality at a given coordinate in Google maps api? I know there are maps with the municipal information, but how to get the municipal of a given point?
You can get information about administrative districts. You want the Geocoding API. The process you are suggesting is generally called 'reverse geocoding'. i.e. going from lat,long to place name.
Information about the response you get, including administrative area types, is available here. Scroll down to
Address Types and Address Component Types.
Exactly how your local 'municipality' will line up with google's schema may take some trial and error.