  Suppose $G$ is a second countable, locally compact, Hausdorff groupoid with a
fixed left Haar system. Let $\go/G$ denote the orbit space of $G$ and $C^*(G)$
denote the groupoid $C^*$-algebra. Suppose that the isotropy groups of $G$ are
amenable. We show that $C^*(G)$ is CCR if and only if $\go/G$ is a $T_1$
topological space and all of the isotropy groups are CCR. We also show that
$C^*(G)$ is GCR if and only if $\go/G$ is a $T_0$ topological space and all of
the isotropy groups are GCR.
