The basis set superposition error-corrected first-order electron densities of several hydrogen bonded complexes of increasing molecular size have been obtained with the Hartree-Fock and density-functional theory versions of the chemical Hamiltonian approach (CHA) methodology. A detailed analysis of the local basis set superposition error (BSSE) effects has been carried out by comparing the uncorrected electron densities and energy components with the CHA ones. Topological analysis of the electron density through the atoms in molecules theory is used in order to obtain a quantitative measure of the BSSE effects in terms of the characterization of the critical points of the electron density. Density difference isocontour maps are also depicted in order to show the local electron density redistributions induced by the BSSE-correction. We show that the effects of the BSSE are common for all the complexes studied, namely water dimer, formic acid dimer and uracil-water complex. The formic acid dimer and uracil-water density difference maps at frozen geometry reveal that the effects of the BSSE do not extend significantly beyond the atoms involved in the interaction and their first neighbors. The main redistribution effects are not strictly localized on the intermolecular region and mostly take place in the valence shells of the heavy atoms directly involved in the intermolecular interaction. These trends are also confirmed by means of an energy decomposition analysis performed at the Hartree-Fock level of theory with the recently proposed chemical energy component analysis (CECA) method. In agreement to previous results, we found that inclusion of diffuse functions is of utmost importance in order to minimize the magnitude of the BSSE. However, both the electron density difference maps and the CECA analysis confirm that the local effects of the BSSE are very different when diffuse functions are present in the calculation.