In this work, circular dichroism in H2 (D2) photoionization is studied in detail. We have selected several photon energies for a case study: 19 eV for which only direct ionization to the 1sσg ionization channel is present, 27 eV where autoionization of Q11Σ+u doubly excited states takes place, and 32.5 eV for which autoionization from Q1 and doubly excited states and direct ionization to 1sσg and 2pσu channels strongly interfere. The latter case shows clear evidence of different behavior of the photoionization against radiation helicity.