  The In-doped topological crystalline insulator Sn$_{1-x}$In$_x$Te 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$_{1-x}$In$_x$Te samples and performed
$^{125}$Te-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 ($1/T_1$) 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.
