In this paper, the potential of a deep learning approach for SAR tomography (TomoSAR) is investigated. TomoSAR is a powerful technique that allows the 3D reconstruction of objects lying on the Earth surface, by separating multiple scatterers with different elevations laying in the same range-azimuth resolution cell. In urban applications, the number of interfering scatterers is typically very small, so that the reconstruction of the elevation reflectivity profile can be faced as a statistical detection problem. Detection performance depends on how well the adopted statistical model fits to the observed scene. For complex urban scenarios this issue can greatly impair achievable accuracy of results. Then, we propose to exploit the neural networks' capabilities to learn the data generative model, in order to face the problem of signal model inaccuracies. In particular, in the assumption of a single scatterer, a neural network can be trained to solve a simple classification problem. Results on simulated and real data are presented.