Co and Na NMR are used to probe the local susceptibility and charge state of the two Co sites of the Na-ordered orthorhombic Na(0.5)CoO(2). Above T(N) = 86 K, both sites display a similar T dependence of the spin shift, suggesting that there is no charge segregation into Co(3+) and Co(4+) sites. Below T(N), the magnetic long range commensurate order found is only slightly affected by the metal-insulator transition at T(MIT) = 51 K. Furthermore, the electric field gradient at the Co site does not change at these transitions, indicating the absence of charge ordering. All these observations can be explained by successive spin-density wave induced by two nestings of the Fermi surface specific to the x = 0.5 Na ordering.