First-principles studies are carried out on the electronic structure and Compton profile for the low-symmetry system of calcium dihydride using the discrete variational local-density-functional method with embedded cluster model. The results demonstrate that, with the ionic bonding picture, experimental data from photoelectron spectroscopy with both x-rays and synchrotron radiation and from Compton profile measurements can be reasonably understood. Based on the bonding character revealed in the electronic structure, we suggest that CaH₂ doped with a monovalent element could be a superconductor.