Vector Quantization (VQ) design for distributed binary decision in the presence of an eavesdropper (Eve) is investigated. An encoder/quantizer (Alice) observes i.i.d. samples and communicates them via a public noiseless rate-limited chan- nel to the detector (Bob) who has also access to a correlated analog source. Bob can take advantage of both informations to perform a binary decision on the joint probability law of these observations. Eve is further assumed to have access to another correlated analog source. This paper evaluates relevant trade-offs between the error probability of the two types and the amount of tolerated information leakage, for the particular case of testing against independence. An application to illustrate our results to real-data measured from the electric consumption at houses to perform anomaly detection is also provided.