  We report $^{195}$Pt-NMR and $^{75}$As-NQR measurements for the locally
non-centrosymmetric superconductor SrPtAs where the As-Pt layer breaks
inversion symmetry while globally the compound is centrosymmetric. The nuclear
spin lattice relaxation rate $1/T_1$ shows a well-defined coherence peak below
$T_c$ and decreases exponentially at low temperatures. The spin susceptibility
measured by the Knight shift also decreases below $T_c$ down to $T<T_c/6$.
These data together with the penetration depth obtained from the NMR spectra
can be consistently explained by assuming a spin-singlet superconducting state
with a full gap. Our results suggest that the spin-orbit coupling due to the
local inversion-breaking is not large enough to bring about an exotic
superconducting state, or the inter-layer hopping interaction is larger than
the spin-orbit coupling.
