No you don't need to get approval from your boss, but be careful to choose the class schedule and handle the study and work in balance.

I had experience of part time study and full time work for a year, it's a very tough journey. Because I wanted to graduate sooner so I still registered 12 units each semester, which would keep a full time student busy alreay, meanwhile the work was very demanding too. So the whole year I got no vacation, no weekends, no relax at all.