A series of high-precision calculations for the electronic structure of MgH have been reported in the past two decades; however, most of them did not include the core-valence correlation and still
exhibit distinct differences. Furthermore, the latest high-precision results have not been applied to the studies of photodissociation dynamics. The primary motivations of this paper are to calculate a more
precise electronic structure of MgH considering a core-valence correlation and to provide the photodissociation cross-sections. The electronic structure of MgH is investigated by multi-reference configuration interaction calculations with Davidson correction (MRCI+Q). We performed two different sets of calculations to investigate
the core-valence correlation and, as a result, obtained accurate potential energy curves (PECs) and transition dipole moments (TDMs). An extrapolation procedure was also employed to eliminate the error of basis set.
Then, the photodissociation cross-sections were calculated using high-precision PECs and TDMs. The PECs and TDMs of the five lowest doublet electronic states, X$^2 B$'^2 E$^2 A$^2 and C$^2 are obtained from calculations including core-valence correlation, termed as CV-MRCI, while PECs of the ten lowest doublet states and three quartet states are also obtained from NCV-MRCI calculations without core-valence correlation. The spectroscopic constants and band oscillator strengths are also provided with high precision levels. The equilibrium $R_e$ and vertical excitation energy $T_e$ are only $0.1<!PCT!>$ different from the measurements. Based on the CV-MRCI results, the rovibrationally resolved photodissociation cross-sections for transitions from X$^2 to the other four states, as well as the total local thermodynamic equilibrium (LTE) cross-sections for temperatures up to 10000 K, are calculated.