In this paper, we investigated the optical Kerr effect (OKE) reduced spectral density (RSD) of liquid and supercooled water at ambient pressure and focused on the contributions of low-density liquid (LDL) and high-density liquid (HDL), which local structures are characterized with tetrahedral order and disorder, respectively. The water systems were generated by performing molecular dynamics (MD) simulations with TIP4P/2005 force fields, and molecules were classified into LDL and HDL with the microscopic structural descriptor [Nature commun. 3 (2014) 3556.]. The OKE RSD was calculated with a model involving the intrinsic polarizabilities of individual molecules and the dipole-induced-dipole mechanism between them. The instantaneous normal mode (INM) analysis was used to dissect the OKE RSD obtained by MD simulations. By considering water as a mixture of LDL and HDL, the OKE RSD in the linearized INM theory is a sum of three contributions, which are resulted from the two partial liquids individually and a cross correlation associated with both of them, in a formulism similar as that for the static structure factor of a binary mixture. By exploring with two separation schemes on the collective polarizability, where they are complemental to each other, the INM analysis provides an insight into the physical causes for the bands in the OKE RSD of liquid and supercooled water and the relation of each band to the local structures of LDL and HDL.