CoO2 is the parent compound for the superconductor NaxCoO2⋅1.3H2O and was widely believed to be a Mott insulator. We performed 59Co nuclear magnetic resonance and nuclear quadrupole resonance studies on LixCoO2 (x=0.35, 0.25, 0.12, and 0.0) to uncover the electronic state and spin correlations in this series of compounds which was recently obtained through electrochemical deintercalation of Li from pristine LiCoO2. We find that although the antiferromagnetic spin correlations systematically increase with decreasing Li content (x), the end member, CoO2, is a noncorrelated metal that well satisfies the Korringa relation for a Fermi liquid. Thus, CoO2 is not simply located at the limit of x→0 for AxCoO2 (A=Li,Na) compounds. The disappearance of the electron correlations in CoO2 is due to the three dimensionality of the compound which is in contrast to the highly two-dimensional structure of AxCoO2.