It depends on where you work. If you are in the restaurant business, your employer must pay you for at least 2 hours when you are scheduled to come in. If you are in the “mercantile trade” (retail or wholesale selling, or work incidental to sales such as buying, delivery, maintenance, office, stock, or clerical work), then you must be paid for at least 4 hours if you are sent home on a scheduled shift. If you work in a beauty shop, a laundry, or the “cleaning and dyeing trade,” then you are also guaranteed 4 hours’ work if you are sent home early. If you believe that your employer has violated these rules, the Connecticut Department of Labor can help you obtain your wages. http://www.ctdol.state.ct.us
Other than those specifically named industries, you are probably only entitled to be paid for the hours that you actually work. Of course, if you have a contract or are in a collective bargaining unit, the rules may be different.