  We study the metric perturbations around the de Sitter and Minkowski
backgrounds in Conformal Gravity. We confirm the presence of ghosts in both
cases. In the de Sitter case, by applying the Maldacena boundary conditions -
the Neumann boundary condition and the positive-frequency mode condition - to
the metric, we show that one cannot recover a general solution for the
perturbations. In turn, alongside the Neumann boundary condition, we derive an
additional condition with which the perturbations of conformal gravity and dS
perturbations of Einstein gravity with cosmological constant coincide. We
further show that the Neumann boundary condition does not lead to a general
solution in Minkowski space. Conversely, we derive the alternative boundary
conditions, with which we attain an agreement between the perturbations of
conformal and Einstein gravity in full generality, thus removing the ghost of
conformal gravity.
