A Raman investigation of the AlH3 polymorph has been carried out at a low temperature (20 K) under helium atmosphere (2 bar). The pristine material was composed of three polymorphs, namely, the alpha, beta, and gamma phases. The beta phase has been removed by warming the sample to 70 degrees C, while further heating at 100 degrees C was used to remove the gamma phase. This allowed us to evidence, on a purely experimental basis, the characteristic Raman spectrum for each phase. Raman spectra, for the three phases, have been also calculated using density functional theory, and the results have been compared to the present experimental data, allowing for a univocal assignment, to each phase, of its characteristic spectral features.