Zero field μSR spectroscopy was applied to a polycrystalline sample of the ferrimagnetic sulfur spinel Fe_0.5Cu_0.5Cr ₂S₄ between 5 and 315 K. The temperature dependence of the interstitial magnetic field B_μ as well as the transverse and longitudinal relaxation rates were deduced. At around 100 K, the temperature dependence of the interstitial field exhibits a strong deviation from the expected Brillouin-like behavior together with a maximum of the transverse relaxation rate. These features are characteristic for a spin reorientation transition. This instability of the ferrimagnetic spin-lattice has not been reported previously. ⁵⁷Fe Mössbauer data from the same sample show no irregularity in the temperature dependence of the Fe hyperfine field which could indicate that the spin reorientation involves primarily the Cr sublattice. Above and below the spin reorientation regime, disorder in the spin-lattice is sizable, but not excessive. At low temperatures, the spins are essentially static, spin dynamics sets in above the reorientation range. The μSR data are also complemented by new susceptibility and magnetization data taken on similar material.