I'm looking for permits of US metropolitan areas, like Chicago, so far I found this one:
Permits issued by the Department of Buildings in the City of Chicago from 2006 to the present
But this one only includes construction permits, I'm also looking for other types of permits like electrical and plumbing
I don't know of any open and free source that publishes this data aggregated across all metropolitan areas, as you found with Chicago this is a type of data that is typically collected and published at the city (or county) level and the particular fields collected and released will differ city from city.
However, building permit data is available for the majority of the largest cities in the US.
For example, you can access New York City building permit data through Enigma here and then from the city government directly here.
If you search building permit data through Enigma you'll find building permit data for a number of other cities including:
Alternately you can visit the department of building or open data portals for each of these cities. Some of these (such as Boston) include electrical and plumbing work permits, others do not.
(Full disclosure: I work for Enigma.)
