In order to clarify the carrier density dependence of the microscopic magnetic nature in Na x CoO 2 · yH 2 O, we have performed a positive muon-spin rotation/relaxation ͑ + SR͒ study of H 2 O and D 2 O intercalated samples. Based on the zero-field ͑ZF͒ + SR measurements, there was no clear difference between the two superconducting phases ͑SCI and SCII͒. This is also likely to exclude the exotic scenario for the superconductivity of the SCII phase, in which the superconducting state breaks the time-reversal symmetry of the Cooper pairs, resulting in the appearance of a weak internal magnetic field below T c . Furthermore, the ZF spectrum for the H 2 O intercalated sample exhibits a clear oscillation in the whole T range measured ͑1.4-100 K͒, suggesting the formation of "͓H 3 O͔ + -like" H 2 + O ions in the sample. The absence of the oscillation in the D 2 O-intercalated sample also evidences the presence of the H 2 + O complex. Considering the fraction of the H 2 + O signal, we have demonstrated the coexistence of ͓H 3 O͔ + ions and H 2 O in this compound.