This work considers mitigation of information leakage between communication and sensing operations in joint communication and sensing systems. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to simultaneously achieve reliable communication and channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to a part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a characteristic of the receiver, e.g., its location. For independent and identically distributed (i.i.d.) states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with a binary joint communication and sensing model.