We investigate the relaxation behavior of thin films of a polyamide random copolymer, PA66/6I, with various film thicknesses using dielectric relaxation spectroscopy. Two dielectric signals are observed at high temperatures, the α process and the relaxation process due to electrode polarization (the EP process). The relaxation time of the EP process has a Vogel-Fulcher-Tammann type of temperature dependence, and the glass transition temperature, T(g), evaluated from the EP process agrees very well with the T(g) determined from the thermal measurements. The fragility index derived from the EP process increases with decreasing film thickness. The relaxation time and the dielectric relaxation strength of the EP process are described by a linear function of the film thickness d for large values of d, which can be regarded as experimental evidence for the validity of attributing the observed signal to the EP process. Furthermore, there is distinct deviation from this linear law for thicknesses smaller than a critical value. This deviation observed in thinner films is associated with an increase in the mobility and/or diffusion constant of the charge carriers responsible for the EP process. The α process is located in a higher-frequency region than the EP process at high temperatures but merges with the EP process at lower temperatures near the glass transition region. The thickness dependence of the relaxation time of the α process is different from that of the EP process. This suggests that there is decoupling between the segmental motion of the polymers and the translational motion of the charge carriers in confinement.