The glass transition temperature and relaxation dynamics of the segmental motions of thin films of polystyrene labeled with a dye, 4-[N-ethyl-N-(hydroxyethyl)]amino-4-nitraozobenzene (Disperse Red 1, DR1) are investigated using dielectric measurements. The dielectric relaxation strength of the DR1-labeled polystyrene is approximately 65 times larger than that of the unlabeled polystyrene above the glass transition, while there is almost no difference between them below the glass transition. The glass transition temperature of the DR1-labeled polystyrene can be determined as a crossover temperature at which the temperature coefficient of the electric capacitance changes from the value of the glassy state to that of the liquid state. The glass transition temperature of the DR1-labeled polystyrene decreases with decreasing film thickness in a reasonably similar manner to that of the unlabeled polystyrene thin films. The dielectric relaxation spectrum of the DR1-labeled polystyrene is also investigated. As thickness decreases, the $alpha$-relaxation time becomes smaller and the distribution of the $alpha$-relaxation times becomes broader. These results show that thin films of DR1-labeled polystyrene are a suitable system for investigating confinement effects of the glass transition dynamics using dielectric relaxation spectroscopy.