  The possible existence of naked singularities, hypothetical astrophysical
objects, characterized by a gravitational singularity without an event horizon
is still an open problem in present day astrophysics. From an observational
point of view distinguishing between astrophysical black holes and naked
singularities also represents a major challenge. One possible way of
differentiating naked singularities from black holes is through the comparative
study of thin accretion disks properties around these different types of
compact objects. In the present paper we continue the comparative investigation
of accretion disk properties around axially-symmetric rotating geometries in
Brans-Dicke theory in the presence of a massless scalar field. The solution of
the field equations contains the Kerr metric as a particular case, and,
depending on the numerical values of the model parameter $\gamma$, has also
solutions corresponding to non-trivial black holes and naked singularities,
respectively. Due to the differences in the exterior geometries between black
holes and Brans-Dicke-Kerr naked singularities, the thermodynamic and
electromagnetic properties of the disks (energy flux, temperature distribution
and equilibrium radiation spectrum) are different for these two classes of
compact objects, consequently giving clear observational signatures that could
discriminate between black holes and naked singularities.
