Multireference single- and double-excitation configuration interaction (MRD-CI) calculations of transition energies for the Hg atom and spectroscopic constants for the HgH molecule are carried out with the generalized relativistic effective core potential (GRECP) method. A new selection criterium for the reference configurations is discussed. The calculated spectroscopic constants are compared with experimental data and results of calculations of other groups. Improvement of accuracy is mainly observed for bond lengths from the GRECP/MRD-CI calculations (without applying the T = 0 correction) with respect to the results of other groups. Analysis of the quality of the approximations employed is carried out.