Double ionization of a polarized atom by a single photon with an arbitrary polarization is theoretically considered. A general expression for the triple differential cross section is obtained and analysed. We point out the existence of a circular and a linear dichroism in the angular distributions of photoelectrons. Generally two types of sources for the dichroism are distinguished: one connected with the initial polarization of the target, and the other related to the two-electron final-state properties. We show how these two types of dichroic effects can be experimentally investigated separately by choosing the detection geometry appropriately. As an example, the photo-double ionization of 2P excited and polarized states of atomic helium is considered. The calculations reveal a measurable dichroism in the angular correlations of two emitted electrons. Possible applications of circular dichroism measurements to the study of superconductors and orbitally ordered materials are discussed.