  We consider Deaconu--Renault groupoids associated to actions of finite-rank
free abelian monoids by local homeomorphisms of locally compact Hausdorff
spaces. We study simplicity of the twisted C*-algebra of such a groupoid
determined by a continuous circle-valued groupoid 2-cocycle. When the groupoid
is not minimal, this C*-algebra is never simple, so we focus on minimal
groupoids. We describe an action of the quotient of the groupoid by the
interior of its isotropy on the spectrum of the twisted C*-algebra of the
interior of the isotropy. We prove that the twisted groupoid C*-algebra is
simple if and only if this action is minimal. We describe applications to
crossed products of topological-graph C*-algebras by quasi-free actions.
