Growing research on re-identification through app usage behavior reveals the privacy threat in having smartphone usage data to third parties. However, re-identifiability of a vulnerable group like the depressed is unexplored. We fill this knowledge gap through an in the wild study on 100 students' PHQ-9 scale's data and 7 days' logged app usage data. We quantify the uniqueness and re-identifiability through exploration of minimum hamming distance in terms of the set of used apps. Our findings show that using app usage data, each of the depressed and non-depressed students is re-identifiable. In fact, using only 7 h' data of a week, on average, 91% of the depressed and 88% of the non-depressed are re-identifiable. Moreover, data of a single app category (i.e., Tools) can also be used to re-identify each depressed student. Furthermore, we find that the rate of uniqueness among the depressed students is significantly higher in some app categories. For instance, in the Social Media category, the rate of uniqueness is 9% higher (P = .02, Cohen's d = 1.31) and in the Health & Fitness category, this rate is 8% higher (P = .005, Cohen's d = 1.47) than the non-depressed group. Our findings suggest that each of the depressed students has a unique app signature which makes them re-identifiable. Therefore, during the design of the privacy protecting systems, designers need to consider the uniqueness of them to ensure better privacy for this vulnerable group.