We analyze differences between ground-state electron densities of a model molecular complex obtained by solving the Kohn-Sham equations with constrained electron density (KSCED) [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] and as a solution of the standard Kohn-Sham equations applied to the whole complex. The differences between KSCED and KS electron densities which result from the inaccuracy of the kinetic energy functional applied in the KSCED equations are discussed. The model molecular complex consists of collinear H2 and HCN molecules separated by a short distance. Several kinetic energy functional approximations are applied within the KSCED framework and the differences between resulting electron densities are studied. The KSCED electron densities depend directly on the functional derivative of the kinetic energy functional applied in the KSCED equations. Among the studied functionals, the one proposed by Zhao et al. [Phys. Rev. A 47, 918 (1993)] and the gradient-dependent functional proposed by Perdew and Wang [Phys. Rev. B 33, 8800 (1986)] led to the smallest differences between KS and KSCED electron densities, thus having the most accurate functional derivative. Both functionals allow one to extend the range of applicability of the KSCED equations to system geometries where an overlap of electron densities of the partners of the complex is significant.