  Scalar fields non--minimally coupled to (2+1)-gravity, in the presence of
cosmological constant term, are considered. Non-minimal couplings are described
by the term $\zeta R \Psi^2$ in the Lagrangian. Within a class of static
circularly symmetric space-times, it is shown that the only existing physically
relevant solutions are the anti-de Sitter space-time for $\zeta=0$, and the
Martinez-Zanelli black hole for $\zeta=1/8$. We obtain also two new solutions
with non-trivial scalar field, for $\zeta=1/6$ and $\zeta=1/8$ respectively,
nevertheless, the corresponding space-times can be reduced, via coordinate
transformations, to the standard anti-de Sitter space.
