What we can tell you
Minnesota licenses specific trades at state level, and those licenses are the file this directory is built from. If a person holds one, you can look them up here or at the department.
What counts as work needing one of those licenses, and what a permit is separately required for, is decided by statute and by your municipality. That is not a question a directory can answer for your particular job.
So: ask your city
Your city's building department answers this for free, and answers it for the actual job you are describing. That is a better answer than anything we could publish.
This is a directory, not a law firm. Nothing here is legal advice, and where the honest answer is “ask your city”, that is what it says.
What you can check right now
If the person gives you a license number, check it. If they hold a state license for the trade, it is in the state's lookup and it is in this directory.
Where this comes from
The department's copy is the live one. Ours is a dated snapshot, and the date is in the footer.