The In-doped topological crystalline insulator Sn_1-xIn_xTe is a promising candidate for a topological superconductor, where it is theoretically suggested that In creates an impurity state responsible for superconductivity. We synthesized high purity Sn_1-xIn_xTe samples and performed ^125Te-nuclear magnetic resonance (NMR) measurements. The NMR spectra under a magnetic field of H_0 = 5 T show a broadening characteristic due to a localized impurity state. The spin-lattice relaxation rate

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... divided by temperature shows a Curie-Weiss like temperature-dependence under H_0 = 0.1 T but is temperature-independent under H_0 = 5 T. These results indicate the existence of quasi-localized impurity states due to In doping.