  We consider the local deformation problem of coisotropic submanifolds inside
Poisson manifolds. To this end the groupoid of coisotropic sections (with
respect to some tubular neighbourhood) is introduced. Although the geometric
content of this groupoid is evident, it is usually a very intricate object.
  We provide a description of the groupoid of coisotropic sections in terms of
a differential graded Poisson algebra, called the BFV-complex. This description
is achived by constructing a groupoid from the BFV-complex and a surjective
morphism from this groupoid to the groupoid of coisotropic sections. The kernel
of this morphism can be easily chracterized.
  As a corollary we obtain an isomorphism between the moduli space of
coisotropic sections and the moduli space of geometric Maurer-Cartan elements
of the BFV-complex.
