The optoelectronic properties of semiconductor quantum-dot (QD) solids depend on the electronic structure of the building blocks and their interactions. Disorder may affect the coupling on a local scale. We have measured the density of states of 2D arrays of PbSe QDs site by site using scanning tunneling spectroscopy. It markedly differs from that of isolated QDs due to electronic coupling in the array. We observe strong local variations in the coupling strength with two prototypical cases: delocalization of the conduction electrons only, and full coupling with both hole and electron delocalization over the QD sites in the array.