This paper describes the behavior of H atoms in laser-crystallized poly-Si for thin-film transistors on liquid crystal display panels, where H atoms were penetrated by plasma hydrogenation in order to improve mobility. Mobility was measured by Hall effect. Si-hydrogen bonds were analyzed by Raman scattering. By short-time hydrogenation, penetrated H atoms terminate dangling bonds as the Si-H configuration largely at grain boundaries, which results in the improvement of mobility. By excessive hydrogenation, Si-H_2 bonds are generated simultaneously with degradation of mobility. Si-H_2 bonds are largely formed at ingrain defects. Hydrogenation using the hot-wire method was also made and it was shown that plasma damage does not take a part of those hydrogenation effects. Origin of correlation among Si-H_2, mobility and amount of in-grain defects was discussed based on impurity scattering and weak-bond models.