This paper presents a global observability analysis of the Switched Reluctance Motor under sensorless operation i.e., only the stator current and voltages are measured. The main contribution of this work is the formal statement of the indistinguishable dynamics of this machine, which describe for the first time, the initial conditions and inputs that cause the loss of observability in this operation condition. The analysis presented concludes that it is impossible to design an observer for every trajectory of the motor. Additionally, there exist singular inputs i.e., inputs that does not distinguish between two initial conditions from the measurements. To illustrate the loss of observability of the Switched Reluctance Motor, some examples are presented.