We report a room-temperature optical reflectivity study performed on [112]-oriented Cd$_3$As$_2$ single crystals over a broad energy range under external pressure up to 10 GPa. The abrupt drop of the band dispersion parameter ($z$-parameter) and the interruption of the gradual redshift of the bandgap at $sim$4~GPa confirms the structural phase transition from a tetragonal to a monoclinic phase in this material. The pressure-induced increase of the overall optical conductivity at low energies and the continuous redshift of the high-energy bands indicate that the system evolves towards a topologically trivial metallic state, although a complete closing of the band gap could not be observed in the studied pressure range. Furthermore, a detailed investigation of the low-pressure regime suggests the possible existence of an intermediate state between 2 and 4~GPa , that might be a precursor of the structural phase transition or due to the lifted degeneracy of the Dirac nodes. Several optical parameters show yet another anomaly at 8~GPa, where low-temperature superconductivity was found in an earlier study.
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