This work deals with the characterization of the conductivity tensor of a carbon fiber reinforced polymer composite (CFRP) thin plate. We propose a contactless method based on the eddy current non destructive testing technique. The used eddy current sensor consists of a ferrite torus on which a winding is wound. The torus is of a rectangular section and contains a thin air-gap in which the thin CFRP plate is inserted. We developed analytical relations giving the longitudinal and transversal conductivities of the CFRP plate as functions of the impedances variations of the eddy current sensor, corresponding to the orientations of the carbon fibers parallel and transverse to the direction of the torus width which is much greater than its thickness. The analytical relations are developed by inverting interpolation functions of curves giving the variations of the sensor impedances as functions of the longitudinal and transversal conductivities of the CFRP plate. These curves are obtained by a numerical model based on a simplified integro-differential formulation in terms of the electric vector potential in the CFRP plate, coupled to the magnetic circuit equations in the ferrite torus. The modeling results are supported by measurements.