Home improvement contractors have to be registerd and follow the law (e.g. have a contract in writing, with a beginning and ending date, etc.). Professionals such as electricians and plumbers, who are otherwised licensed (and performing services within their domain) do not have to register or comply.
The exemption that you are referring to in Section 20-428 of the Connecticut General Statutes only exempts people who hold one of the professional or occupational licenses set foth in Chapters 369 through 400 of the General Statutes. These include licenses for such professions as architects, professional engineers and surveyors, electricians, plumbers, heating and air conditioning contractors, landscape architects, septic system installers, and other. The statute that you are referring to only exempts people who hold these types of professional and occupational licenses (take a look at Chapters 369 through 400 for the entire list of professional and occupational licenses); and only to the extent that such person engages in such work for which he is licensed or registered. Thus, the Home Improvement laws set forth in Sections 20-418, etc. apply to contractors who engage in home improvement (as that term is defined in Section 20-419), except for persons who hold one of the specific professional or occupational licenses listed in Chapters 369 through 400, and the exception only covers specific work for which such person holds a license. (for example: if a licensed electrician offers to remodel the entire kitchen, he would not be exempt from complying with the requirements of the home improvement laws, because he would be performing work that goes beyond the area of his license.)