  Yes it does ! Indeed an extended version of Levinson's theorem is proposed
for a system involving complex eigenvalues. The perturbed system corresponds to
a realization of the Schroedinger operator with inverse square potential on the
half-line, while the Dirichlet Laplacian on the half-line is chosen for the
reference system. The resulting relation is an equality between the number of
eigenvalues of the perturbed system and the winding number of the scattering
system together with additional operators living at 0-energy and at infinite
energy.
