We report the results of μSR measurement of the re-entrant spin-glass thiospinel CuCrZrS₄. We have observed a relatively small enhancement of the relaxation rate at T_C∼60 K but no oscillations in the time spectra in the first magnetic phase between T_C and T_f∼7 K, suggesting that the first magnetic phase is not a long-range ordering state. A fast depolarization component in ZF-μSR appears around 40 K and develops accompanied by the rapid increase of its relaxation rate with decreasing temperature down to T_f. The fast depolarization component is interpreted as the signature of the magnetic correlation attributed to the re-entrant spin-glass behavior. At all the measured temperatures, there remain relaxations even at high magnetic fields, revealing a dynamical local field due to strong magnetic correlations.