A theoretical investigation of the angular distributions of photoelectrons (ADP) ejected from fixed-in-space molecules or clusters having C-2v symmetry is presented. The consideration is based on an expansion of the photoelectron wave functions in symmetry-adapted spherical harmonics. The ADP is derived for linearly polarized, circularly polarized, and unpolarized light in the case when the light beam is parallel to the C-2 axis of the molecule. The twofold symmetry of the target reveals itself most clearly for circularly polarized or unpolarized light if the dependence on the azimuthal angle is studied for a fixed polar angle. The circular dichroism in the angular distribution (CDAD) is investigated for the general case of an arbitrary direction of the photon beam. It is shown on model examples that the CDAD has characteristic zeros in the mirror planes of the molecule that may be used to determine the symmetry of the initial state. For linearly polarized light the photoelectron angular distributions have a more complicated dependence on the azimuthal angle, though it also may be used to distinguish between different initial states. The examples presented in this paper demonstrate the general properties of the angular distributions as well as properties of the circular and linear dichroism in the angular distribution.