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 $alpha$-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, $T_{rm g}$, evaluated from the EP-process agrees very well with the $T_{rm g}$ 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 $alpha$-process is located in a high 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 $alpha$-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.