The second harmonic and electro-optical responses for the water molecule in its liquid state are theoretically revised. The continuum, semicontinuum, and supermolecular solvation models are employed using quadratic response theory at the Hartree-Fock level, either in the equilibrium or nonequilibrium implementation. The experimentally observed sign change of the second harmonic response of water on liquefaction is reproduced using the supermolecular and semicontinuum model for both equilibrium and nonequilibrium solvation. The conclusions of a previous study, which rested upon linear response theory in an equilibrium implementation, are confirmed. Also, the assumption of Kleinman symmetry and dispersion is addressed.