We show that the \(C^*\) -algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex \(*\) -algebra is simple. We also improve on Steinberg and Szakács’s algorithm to determine if the \(*\) -algebra is simple. This provides an interesting class of non-Hausdorff, amenable, effective and minimal ample groupoids for which simplicity of the \(C^*\) -algebra and the complex \(*\) -algebra are equivalent.
