We have studied electronic properties of perovskite oxyhydrides ATiO_3–xH_x (A = Ba, Sr). Epitaxial thin films of ATiO_3–xH_x with various hydride compositions, up to x = 0.58 for Ba and x = 0.45 for Sr, are prepared by the low-temperature CaH₂ reduction of the corresponding oxide films deposited on (LaAlO₃)_0.3(SrAl_0.5Ta_0.5O₃)_0.7 (LSAT) substrates by pulsed laser deposition. Resistivity measurements for A = Sr show a metallic phase over a wide range of H^– composition, implying a substantial stabilization of H 1s orbitals that should be distributed over O 2p orbitals. On the other hand, for A = Ba, a semiconducting behavior is seen up to ∼5–8% of H– substitution. Interestingly, a similar contrasting behavior is observed in a Nb-substituted BaTiO₃ and SrTiO₃, which suggests that a local cation–off centering in lightly doped Ba films creates in-gap states in the band structure (as opposed to the Sr films), hindering the electron transport.