  Well-known work of Renault shows that if $\mathcal{E}$ is a twist over a
second countable, effective, \'etale groupoid $G$, then there is a naturally
associated Cartan subalgebra of the reduced twisted groupoid C*-algebra
$C^*_{r}(G; E)$, and that every Cartan subalgebra of a separable C*-algebra
arises in this way. However twisted C*-algebras of non-effective groupoids $G$
can also possess Cartan subalgebras: In work by the first author together with
Gillaspy, Norton, Reznikoff, and Wright, sufficient conditions on a subgroupoid
$S$ of $G$ were found that ensure that $S$ gives rise to a Cartan subalgebra in
the cocycle-twisted C*-algebra of $G$. In this paper, we extend these results
to general twists $\mathcal{E}$, and we refine the conditions on the
subgroupoid for $C^*_{r}(S;\mathcal{E}_S)$ to be a Cartan subalgebra of
$C^*_{r}(G;\mathcal{E})$.
