The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun's disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle a of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and a patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of a of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the a pattern of the clear sky. Under overcast conditions the value of a is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low (p <= 16 %). Our results obtained under overcast conditions complete the earlier findings that the a pattern of the clear sky also appears in partly cloudy, foggy, and smoky skies. Our results show that the celestial distribution of the direction of polarization is a very robust pattern being qualitatively always the same under all possible sky conditions. This is of great importance for the orientation of polarization-sensitive animals based on sky polarization under conditions when the Sun is not visible. (c) 2007 Optical Society of America.