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)center dot 6(6) topology, it shows an ABX(3) 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 non-centrosymmetric (S.G.: Pna2(1)) and displays a polar aixs. 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 mu C/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 mu C/cm(2). As shown by second harmonic generation studies, this net polarization can be greatly increased by applying pressure (P-max = 14 GPa), an external stimulus that, in turn, induces the appearance of new structural phases, as confirmed by Raman spectroscopy.