This paper presents the closed-form analytical determination of the current signature of a surface-mounted permanent magnet synchronous motor drive controlled by means of field oriented control strategy, when a fault occurs in one or more current sensors. Both DC offset and gain fault for all phase current sensors are considered. The proposed model includes the response of the control loop and related gains, eliminating the need for phase voltage sensors and complicated state estimation. However, the proposed approach requires the solution of an overdetermined system of equations. Then a new methodology of solution is proposed to save computing time, as an alternative to the classical one based on the Moore-Penrose pseudoinverse matrix. Experimental results and sensitivity analysis to parameter variations confirm the validity of the proposed model.