The Chemical Hamiltonian Approach (CHA) versions of the Roothaan and Kohn-Sham equations, labeled CHA/F and CHA/DFT, respectively, have been used to obtain the basis set superposition error (BSSE)-corrected first-order electron density of the hydrogen fluoride dimer with several basis sets. We have analyzed the effect of BSSE in terms of the electronic relaxation, i.e., the redistribution of the electron density due to the inclusion of the CHA correction at a frozen geometry, along with the subsequent nuclear relaxation process. Critical points of the charge density have been located and characterized to compare the conventional, uncorrected first-order electron density against the BSSE-corrected density at each level of theory. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane have also been plotted to gain insight into the effects of BSSE correction on the electron density.