Ab initio CI calculations have been carried nut for the low-energy states of the mercury hydride molecule HgH and its isotopomers. A relativistic effective core potential (RECP) given by Ross et al. [J. Chem. Phys. 93, 6654 (1490)] is employed to describe all but the Hg 5d and 6s valence electrons. Tests for a series of low-lying states of Hg, Hg+, and Hg2+ demonstrate that 0.1 eV accuracy is obtained at the SCF level with a high-quality basis set for this RECP in comparison with all-electron Dirac-Fock results up to 32 eV excitation energy. The DF values are themselves in error by 1-3 eV on the average compared to experiment, but the present CI calculations based on this RECP lead to considerably higher accuracy because of the importance of correlation effects in such determinations. Energy differences (12 cases) between states with the same number of electrons are computed to an accuracy of 0.1-0.2 eV in all cases after the spin-orbit interaction is included. These results compare favorably with those obtained by Haussermann et al. [Mol. Phys. 78, 1211 (1993)] with a ... 5s(2)5p(6)5d(10)6s(2)RECP and a corresponding larger AO basis to describe the more tightly bound electrons. Good agreement is found for the spectroscopic co constants of the HgH molecule in its lowest four electronic states : X (2) Sigma(1/2)(+), A(1) (2) Pi(1/2), A(2) (2) Pi(3/2), and B (2) Sigma(1/2)(+) (maximal errors of 1000 cm(-1) for T-e, 0.03 Angstrom for r(e) and 150 cm(-1) for omega(e)). An RKR curve reported for the A(1) state is shown to be in error beyond r=4.0 alpha(0) because of its failure to describe a key avoided crossing with the B state. Radiative lifetimes computed for the A (2) Pi multiplets are both found to agree with values deduced from experiment to within 40%. The calculations find no difference in the HgH and HgD radiative lifetimes for either the A(1) or the A(2) states, whereas a large distinction in the measured A(1) lifetimes of the two isotopomers is observed, thereby supporting the previous experimental conclusion that strong predissociation occurs in the HgH A(1) state. Numerous higher-lying electronic states are also studied, with T-e values up to 60 000 cm(-1), and on this basis it is argued that earlier assignments for the HgH C-X and D-X transitions are incorrect, as previously concluded by Nedelec et al. [Chem. Phys. 134, 137 (1989)].