  We have performed $^{119}$Sn-NMR measurements on the antiperovskite oxide
superconductor Sr$_{3-x}$SnO to investigate how its normal state changes with
the Sr deficiency. A two-peak structure was observed in the NMR spectra of all
the measured samples. This suggests that the phase separation tends to occur
between the nearly stoichiometric and heavily Sr-deficient Sr$_{3-x}$SnO
phases. The measurement of the nuclear spin-lattice relaxation rate $1/T_1$
indicates that the Sr-deficient phase shows a conventional metallic behavior
due to the heavy hole doping. In contrast, the nearly stoichiometric phase
exhibits unusual temperature dependence of $1/T_1$, attributable to the
presence of a Dirac-electron band.
