We studied the H vibrations in H-doped YBa₂Cu₃O_xH_y, (y=0.6) by neutron spectroscopy. Neutron spectra were taken at 10 and 14 K from both orthorhombic (x approximately=6.9) and tetragonal (x approximately=6.3) samples. The spectra exhibit large H-induced intensities in the energy range between 40 and 130 meV. In comparison to orthorhombic samples, the H vibrations in tetragonal samples are shifted to lower energies by approximately 11%. This shift is opposite to the spectral shift of the lattice vibrations between H-free orthorhombic and tetragonal YBa₂Cu₃O_x, frequently attributed to differences in the electron-phonon coupling. Our results show that any such differences in the electron-phonon coupling are not apparent in the H vibrations. The results also support previous suggestions that the H occupies sites in the close neighbourhood of the Cu(l) atomic planes.