We investigate the anisotropy in the complex conductivity of a clayrock formation through both laboratory and in situ measurements. Laboratory measurements have been conducted on four samples from two cores of the Callovo-Oxfordian formation from the Paris Basin (France). This clay-rock formation is anisotropic with a well-defined bedding plane. Two of the cylindrical core samples are taken in the transverse direction with respect to the bedding plane while two other core samples are taken in the in-plane direction. The complex conductivity spectra are performed in the frequency range 20 mHz to 45 kHz and in a broad pore water saturation range from near saturation to a residual saturation of ~25%. The complex conductivity spectra are fitted with a double Cole Cole model, the low-frequency contribution corresponding to induced polarization effect while the high-frequency contribution is related to the Maxwell-Wagner polarization. The six Cole Cole parameters are investigated as a function of saturation and we evaluate their degree of anisotropy versus the effect of saturation. The low-frequency instantaneous conductivity and normalized chargeability show a consistent degree of anisotropy with an anisotropy ratio equal to 3.8 ± 0.5 for one core sample and 6.5 ± 0.9 for the second core sample. These values represent a substantial level of anisotropy. The low-frequency Cole Cole exponent and relaxation time do not show substantial amount of anisotropy. The monitoring of the evolution of the weight in the controlled humidity chamber seems to indicate that their relative permeabilities do not show a strong anisotropic behavior. Finally, the laboratory data are discussed in the context of field data obtained with an azimuthal array of 12 electrodes.