  The complement of the hyperplanes $\{x_i=x_j\}$, for all $i\neq j$ in $M^n$,
for $M$ an aspherical $2$-manifold, is known to be aspherical. Here we consider
the situation, when $M$ is a $2$-dimensional orbifold. We prove this complement
to be aspherical for a class of aspherical $2$-dimensional orbifolds, and
predict that it should be true in general also. We generalize this question in
the category of Lie groupoids, as orbifolds can be identified with a certain
kind of Lie groupoids.
