Exploitation of X-ray circular polarized beams to study forbidden Bragg reflections and new information that could be obtained in these experiments are discussed. It is shown that the intensities of such reflections can be different for the right- and left-circular polarizations (i.e. exhibiting circular dichroism) even for the dipole-dipole resonant transitions involved in the scattering process. This difference can be observed only in crystals having no center of inversion. Here, this approach is used to study helicity-dependent resonant diffraction in copper metaborate CuB2O4 single crystal, which is non-centrosymmetric but achiral. Nonetheless, a strong circular dichroism has been observed for hh0 forbidden reflections in the vicinity of the Cu K-edge. This effect is shown to originate from dipolar transitions in Cu atoms occupying the 8(d) Wyckoff position only.