Let $\mathcal{O}$ be a finite-dimensional, paracompact, Hausdorff, smooth (and compact, if it helps) orbifold. Is there an isomorphism between the real Čech cohomology and singular cohomology **of the underlying space** $|\mathcal{O}|$?


(NB. The answers of Simon Rose and David C refer to an earlier version of the question and relate the Čech cohomology of the orbifold $\mathcal{O}$ to the singular cohomology of it's underlying space $|\mathcal{O}|$)



Is the Čech cohomology of an orbifold isomorphic to its singular cohomology?
It's a classical result that if $X$ is paracompact and locally contractible, then singular cohomology and Cech cohomology of $X$ coincide, with coefficients in any abelian group. A reference is Spanier's textbook. This applies in particular to the underlying space of an orbifold, in which case a small neighborhood of any point is the cone on the link of the point. 


