In this work, we focus on [(CH3)2NH2]PbI3, a member of the [AmineH]PbI3 series of hybrid organic-inorganic compounds, reporting a very easy mechanosynthesis route for its preparation at room temperature. We report that this [(CH3)2NH2]PbI3 compound with 2H-perovskite structure experiences a first-order transition at ≈250 K from hexagonal symmetry P63/mmc (HT phase) to monoclinic symmetry P21/c (LT phase), which involves two cooperative processes: an off-center shift of the Pb2+ cations and an order-disorder process of the N atoms of the DMA cations. Very interestingly, this compound shows a dielectric anomaly associated with the structural phase transition. Additionally, this compound displays very large values of the dielectric constant at room temperature because of the appearance of a certain conductivity and the activation of extrinsic contributions, as demonstrated by impedance spectroscopy. The large optical band gap displayed by this material (Eg = 2.59 eV) rules out the possibility that the observed conductivity can be electronic and points to ionic conductivity, as confirmed by density functional theory calculations that indicate that the lowest activation energy of 0.68 eV corresponds to the iodine anions, and suggests the most favorable diffusion paths for these anions. The obtained results thus indicate that [(CH3)2NH2]PbI3 is an electronic insulator and an ionic conductor, where the electronic conductivity is disfavored because of the low dimensionality of the [(CH3)2NH2]PbI3 structure.