  We report the $^{121/123}$Sb-NMR/nuclear quadrupole resonance (NQR)
measurements on the newly-discovered superconductor BaTi$_2$Sb$_2$O with a
two-dimensional Ti$_2$O square-net layer formed with Ti$^{3+}$ (3$d^1$). NQR
measurements revealed that the in-plane four-fold symmetry is broken at the Sb
site below $T_{\rm A} \sim$ 40 K, without an internal field appearing at the Sb
site. These exclude a spin-density wave (SDW)/ charge density wave (CDW)
ordering with incommensurate correlations, but can be understood with the
commensurate CDW ordering at $T_{\rm A}$. The spin-lattice relaxation rate
$1/T_1$, measured at the four-fold symmetry breaking site, decreases below
superconducting (SC) transition temperature $T_{\rm c}$, indicative of the
microscopic coexistence of superconductivity and the CDW/SDW phase below
$T_{\rm A}$. Furthermore, $1/T_1$ of $^{121}$Sb-NQR shows a coherence peak just
below $T_{\rm c}$ and decreases exponentially at low temperatures. These
results are in sharp contrast with those in cuprate and iron-based
superconductors, and strongly suggest that its SC symmetry is classified to an
ordinary s-wave state.
