We investigated magnetization, muon spin rotation and relaxation (µSR), and ¹¹⁹Sn Mössbauer spectroscopy on Sn substituted CuCr_2-xSn_xS₄ (x = 0.03 and 0.08) spinel compounds. The magnetization and µSR results reveal similar additional low-temperature magnetic transitions around 80 K and 40 K as found for the undoped material, indicating a magnetic ground state deviating from a simple collinear ferromagnet. The observed changes in the Mössbauer spectra are less pronounced and are discussed in view of the different positions of the local probes µ⁺ and ¹¹⁹Sn and their different magnetic coupling to the magnetic Cr lattice. Above 80 K, both µSR and Mössbauer spectra show temperature-dependent inhomogeneous broadening either due to structural or charge disorder and changing spin dynamics that can be related to a precursor magnetic phase above the well-defined static low-temperature phase.