In this paper we investigate multimodal biometric person and object identification. We model this process of multimodal identification as multimodal multiple hypothesis testing with independent modalities. We analyze theoretical performance limits that can be attained in such a multimodal protocol in terms of exponents of average error probability. Furthermore, we address a privacy related issues in this paper. In particular, we consider performance/privacy trade-off due to the indirect multimodal identification performed in a secret subspace and approximate the obtained performance limits using properties of random projections. Finally, a set of experiments exemplifies our findings.