Excited configurations of hydrogen in the oxyhydride BaTiO_3−xH_x (x=0.1–0.5), which are considered to be involved in its hydrogen transport and exchange processes, were investigated by positive muon spin relaxation spectroscopy using muonium (Mu) as a pseudoisotope of hydrogen. Muons implanted into the BaTiO_3−xH_x perovskite lattice were mainly found in two qualitatively different metastable states. One was assigned to a highly mobile interstitial protonic state, which is commonly observed in perovskite oxides. The other was found to form an entangled two spin-12 system with the nuclear spin of an H⁻ ion at the anion site. The structure of the (H,Mu) complex agrees well with that of a neutralized center containing two H⁻ ions at a doubly charged oxygen vacancy, which was predicted to form in the SrTiO_3−δ perovskite lattice by a computational study [Y. Iwazaki et al., APL Mater. 2, 012103 (2014)]. Above 100 K, interstitial Mu+ diffusion and retrapping to a deep defect were observed, which could be a rate-limiting step of macroscopic Mu/H transport in the BaTiO_3−xH_x lattice.