We have studied the dielectric responses of the layered cobalt oxysulfide Sr2Cu2CoO2S2 with the CoO2 square-planes. With decreasing temperature below the Néel temperature, the resistivity increases like a semiconductor, and the thermopower decreases like a metal. The dielectric constant is highly dependent on temperature, and the dielectric relaxation is systematically changed with temperature, which is strongly correlated to the magnetic states. These behaviors suggest that carriers distributed homogeneously in the paramagnetic state at high temperatures are expelled from the antiferromagnetically ordered spin domain below the Néel temperature.