We report ^59Co NMR studies in single crystals of cobalt oxide superconductor Na_0.42CoO_2·1.3H_2O (T_c=4.25K) and its parent compound Na_0.42CoO_2. We find that both the magnitude and the temperature (T) dependence of the Knight shifts are identical in the two compounds above T_c. The spin-lattice relaxation rate (1/T_1) is also identical above T_0 ∼60 K for both compounds. Below T_0, the unhydrated sample is found to be a non-correlated metal that well conforms to Fermi liquid theory, while

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... in fluctuations develop in the superconductor. These results indicate that water intercalation does not change the density of states but its primary role is to bring about spin fluctuations. Our result shows that, in the hydrated superconducting compound, the in-plane spin fluctuation around finite wave vector is much stronger than that along the c-axis, which indicates that the spin correlation is quasi-two-dimensional.