  The existence of a regular non-trivial scalar field in the background of an
asymptotically flat static reflecting star is discussed. The scalar field is
assumed to be conformally coupled to the outside matter. The induced scalar
charge is determined and the required conditions to have regular field are
obtained. The results are compared with the case of a black hole. Conditions to
have regular non-trivial scalar field out of the black hole horizon are
investigated. We show that in the presence of a scalar source, in contrast to
the black holes, the reflecting star becomes polarized.
