The goal of this paper is to design a statistical test for the camera model identification problem from JPEG images. The approach relies on the camera fingerprint extracted in the Discrete Cosine Transform (DCT) domain based on the state-of-the-art model of DCT coefficients. The camera model identification problem is cast in the framework of hypothesis testing theory. In an ideal context where all model parameters are perfectly known, the Likelihood Ratio Test is presented and its performances are theoretically established. For a practical use, two Generalized Likelihood Ratio Tests are designed to deal with unknown model parameters such that they can meet a prescribed false alarm probability while ensuring a high detection performance. Numerical results on simulated and real JPEG images highlight the relevance of the proposed approach.