We describe in this paper a Two-Stream Siamese Neural Network for vehicle re-identification. The proposed network is fed simultaneously with small coarse patches of the vehicle shape's, with 96 x 96 pixels, in one stream, and fine features extracted from license plate patches, easily readable by humans, with 96 x 48 pixels, in the other one. Then, we combined the strengths of both streams by merging the Siamese distance descriptors with a sequence of fully connected layers, as an attempt to tackle a major problem in the field, false alarms caused by a huge number of car design and models with nearly the same appearance or by similar license plate strings. In our experiments, with 2 hours of videos containing 2982 vehicles, extracted from two low-cost cameras in the same roadway, 546 ft away, we achieved a F-measure and accuracy of 92.6% and 98.7%, respectively. We show that the proposed network, available at https://github.com/icarofua/siamese-two-stream, outperforms other One-Stream architectures, even if they use higher resolution image features.