We report a complete study of the lattice dynamics, dielectric, elastic and piezoelectric properties of hexagonal semiconducting chromium disilicide (CrSi₂). From a combined experimental and theoretical study, we have revisited the phonon mode assignments at the zone-center, so that the contradictions met in previous experimental studies between 250 and 300 cm⁻¹ are now explained and understood. We found that the temperature dependence of the Raman frequencies is mainly due to an implicit volume contribution and related to the large Grüneisen parameter. This explains why CrSi₂ has a moderate thermal conductivity although its Debye temperature is quite large. Optic and static dielectric constants have also been analyzed and discussed. The elastic constants of CrSi₂ are large, but this compound is quite brittle. In addition, the relatively low Poisson coefficient associated to the large negative Cauchy pressure of CrSi₂ indicate the angular nature of its bonding. The calculation of its piezoelectric coefficient shows a sizable value with a magnitude similar to that reported for α-quartz. This prediction requires, however, experimental confirmation.