  Let G be a (not necessarily Hausdorff) locally compact groupoid. We introduce
a notion of properness for G, which is invariant under Morita-equivalence. We
show that any generalized morphism between two locally compact groupoids which
satisfies some properness conditions induces a C*-correspondence from
$C*_r(G_1)$ to $C^*_r(G_2)$, and thus two Morita equivalent groupoids have
Morita-equivalent $C^*$-algebras.
