Layered perovskite titanium oxyhydrides have been prepared by low-temperature topochemical CaH2 reduction from Ruddlesden-Popper Srn+1TinO3n+1 phases (n = 1, 2) and structurally characterized by combined synchrotron X-ray and neutron diffraction data refinements. In the single-layered Sr2TiO3.91(2)D0.14(1) material, hydride anions are statistically disordered with oxides on the apical site only, as opposed to known transition-metal oxyhydrides exhibiting a preferred occupation of the equatorial site. This unprecedented site selectivity of H- has been reproduced by periodic DFT+U calculations, emphasizing for the hydride defect a difference in formation energy of 0.24 eV between equatorial and apical sites. In terms of electronic structure, the model system SSr2TiO3.875H0.125 is found to be slightly metallic and the released electron remains mostly delocalized over several Ti atoms. On the other hand, hydride anions in the double-layered Sr3Ti2O6.20H0.12 material show a clear preference for the bridging apical site within the perovskite slabs, as confirmed by DFT calculations on the Sr3Ti2O6.875H0.125 model system. Finally, the influence of the B-site chemical nature on the hydride site selectivity for early 3d transition metals is theoretically explored in the single-layered system by substituting vanadium for titanium. The V3+ electronic polaron is suggested to play a role in stabilizing H- on the equatorial site in Sr2VO4-xHx for x = 0.125.