  After a brief description of the $\mathbb{Z}$-graded differential Poisson
algebra, we introduce a covariant star product for exterior differential forms
and give an explicit expression for it up to second order in the deformation
parameter $\hbar$, in the case of symplectic manifolds. The graded differential
Poisson algebra endows the manifold with a connection, not necessarily
torsion-free, and places upon the connection various constraints.
