The permittivity tensor of low-symmetry crystals could be essentially anisotropic in the soft-X-ray region if the wavelength is close to some atomic core level absorption edge. Simple Fresnel's formulae are generally invalid in this case for calculations of the X-ray reflectivity, and a number of effects well known in crystal optics occur. The method of permittivity tensor calculations near the K absorption edge is proposed in the present paper. The method is used in order to study the dependence of the X-ray reflectivity fine structure on the polarization and orientation of the incident wave in the case of a uniaxial crystal and small glancing angles. It is shown that, using such dependences, one could obtain complete information about the atomic scattering factor tensor in the crystal in the anomalous dispersion region. The X-ray reflectivity fine structure for different faces of a hexagonal BN crystal has been calculated and compared with experiment. The results obtained have shown evidence of strong crystal optic effects in the case treated.