It may a stupid question. As stated in Lang-Fang Wu' paper (JDG 33(1991)) “Bad orbifolds do not admit metrics of constant curvature. ” Can anyone give a proof or a reference about this statement. How about the case for high-dim orbifold? Thank you for any comments.

（An orbifold is called bad if it can not be covered by a manifold. For example, the only closed bad 2-orbifold are teardrops and (p,q)-footballs, for which they have only one singular point with order $n$ and two singular points with order $p,q$(which are coprime numbers) resp.）