Recently, a superconducting (SC) transition from low-field (LF) to high-field (HF) SC states was reported in CeRh_{2}As_{2}, indicating the existence of multiple SC states. It has been theoretically noted that the existence of two Ce sites in the unit cell, the so-called sublattice degrees of freedom owing to the local inversion symmetry breaking at the Ce sites, can lead to the appearance of multiple SC phases even under an interaction inducing spin-singlet superconductivity. CeRh_{2}As_{2} is considered as the first example of multiple SC phases owing to this sublattice degree of freedom. However, microscopic information about the SC states has not yet been reported. In this study, we measured the SC spin susceptibility at two crystallographically inequivalent As sites using nuclear magnetic resonance for various magnetic fields. Our experimental results strongly indicate a spin-singlet state in both SC phases. In addition, the antiferromagnetic phase, which appears within the SC phase, only coexists with the LF SC phase; there is no sign of magnetic ordering in the HF SC phase. The present Letter reveals unique SC properties originating from the locally noncentrosymmetric characteristics.