We report on the hybrid inorganic-organic ammonium compound [NH4][Cd(HCOO)3], which displays a most unusual framework structure: instead of the expected 4(9)·6(6) topology, it shows an ABX3 perovskite architecture with the peculiarity and uniqueness (among all the up-to-date reported hybrid metal formates) that the Cd ions are connected only by syn-anti formate bridges, instead of anti-anti ones. This change of the coordination mode of the formate ligand is thus another variable that can provide new possibilities for tuning the properties of these versatile functional metal-organic framework materials. The room-temperature crystal structure of [NH4][Cd(HCOO)3] is noncentrosymmetric (S.G.: Pna21) and displays a polar axis. DFT calculations and symmetry mode analysis show that the rather large polarization arising from the off-center shift of the ammonium cations in the cavities (4.33 μC/cm(2)) is partially canceled by the antiparallel polarization coming from the [Cd(HCOO)3](-) framework, thus resulting in a net polarization of 1.35 μC/cm(2). As shown by second harmonic generation studies, this net polarization can be greatly increased by applying pressure (Pmax = 14 GPa), an external stimulus that, in turn, induces the appearance of new structural phases, as confirmed by Raman spectroscopy.