We report Pt-195-NMR and As-75 nuclear quadrupole resonance measurements for the locally noncentrosymmetric 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 Tc down to T < T-c/6. These data, together with the penetration depth obtained from the NMR spectra, can be consistently explained by a spin-singlet superconducting state with a full gap. Our results suggest that the spin-orbit coupling due to the local inversion-symmetry breaking is not large enough to bring about an exotic superconducting state, or the interlayer hopping interaction is larger than the spin-orbit coupling.
