  We prove that the spectrum of the Kohn Laplacian does not determine the
equivalence classes of CR manifolds. We construct pairs of odd-dimensional
elliptic manifolds that are not equivalent as CR manifolds but whose Kohn
Laplacians have the same spectrum. These manifolds are endowed with the CR
structures inherited from the canonical CR structure on the sphere of the same
dimension. We provide three different constructions among lens spaces and an
additional one among elliptic manifolds with non-cyclic fundamental groups.
