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Accurate prediction of spin-state energy difference is crucial for understanding the spin crossover (SCO) phenomena and is very challenging for the density functional approximations, especially for the local and semi-local approximations, due to delocalization errors. Here, we investigate the effect of self-interaction error removal from the local spin density approximation (LSDA) and PBE generalized gradient approximation (GGA) on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, which recovers uniform electron gas limit of underlying functional and approaches the well-known Perdew-Zunger self-interaction correction [Phys. Rev. B, 23, 5048 (1981)] (PZSIC) as a special case when the scaling factor is constant. Our results, when compared with reference diffusion Monte Carlo (DMC) results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon DFAs. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, like CCSD(T), gives a correct sign of spin-state gaps for all ligands with MAE of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).