Let $X$ be an Artin stack over the complex numbers. What can one say analytically locally on the coarse space $\left|X\right|$ about the structure of $X$? For example, can one say that $X=U/G$ where $G$ is an algebraic group acting on a scheme or complex analytic space $U$? I actually suspect that this is false, and that a counterexample is given by the moduli stack of nodal genus zero curves (I don't see how to construct such a neighborhood around $\mathbb CP^1\vee\mathbb CP^1$). If it is indeed false, what is the best one can say?

A related question: Stacks as local quotients or via atlases