Let
![$G$](img16.png)
be the circulant graph
![$C_n(S)$](img17.png)
with
![$S\subseteq\{ 1,\ldots,\left \lfloor\frac{n}{2}\right \rfloor\}$](img18.png)
and let
![$\Delta$](img19.png)
be its independence complex. We describe the well-covered circulant graphs with 2-dimensional
![$\Delta$](img19.png)
, and construct an infinite family of vertex-decomposable circulant graphs within this family. Moreover, we show that if
![$C_n(S)$](img17.png)
has a 2-dimensional vertex decomposable
![$\Delta$](img19.png)
, then it has a level Stanley-Reisner ring.