We report results of magnetic and ultrasound studies of the sulfide spinel CoCr₂S₄, for which the multiferroicity has recently been suggested. Clear anomalies in the magnetic and acoustic properties have been observed at T_N = 222 K and in applied magnetic fields evidencing the important role of magnetoelastic interactions in this material. In contrast, no anomalies have been detected at T_C = 28 K, where a spontaneous electric polarization and isostructural distortions have been reported. We have extracted the H-T phase diagram of CoCr₂S₄ from our experiments for magnetic fields applied along the 111 direction. We discuss our observations in relation to our earlier results obtained for the oxide multiferroic spinel CoCr₂O₄.