This technical note addresses the distinguishability problem for continuous linear time-invariant systems using their input and output data. The proposed approach is based on the characterization of the class of initial state vectors and control input signals that make the outputs of different continuous linear time-invariant systems indistinguishable. This class is defined here as the indistinguishability zone. From this characterization, a simple necessary and sufficient condition for the distinguishability of single-input, single-output systems is established. Furthermore, it is shown that multiple-input, single-output systems are never distinguishable.