  We introduce and investigate the notion of a $\mathbb Z$-graded covering for
a supermanifold. More precisely, Donagi and Witten suggested a construction of
the first obstruction class for splitting of a supermanifold via differential
operators. We prove that an infinite prolongation of this construction
satisfies some universal properties and can be seen as a covering of a
supermanifold in the category of graded manifolds.
