An application of holography for the investigation of surface relief by the method of attenuated total internal reflection is reported. A theoretical proof is given of the possibility of recording the phase change of the object light wave that is totally internally reflected from regions where there is no optical contact with the object or undergoes attenuated total reflection from regions where the relief allows for an optical contact. An experimental investigation is described of the dependence of the diffraction efficiency of the recorded hologram of a fingerprint on the ratio between the intensities of the object and reference waves.