Hochschild cohomology of dg manifolds associated to integrable distributions

For the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$, and an integrable distribution $F\subseteq T_M{\otimes }_{\mathbb{R}}\mathbb{K}$ on a smooth manifold $M$, we study the Hochschild cohomology of the dg manifold $(F[1],d_F)$ and establish a canonical isomorphism with the Hochschild cohomology of the algebra of functions on leaf space in terms of transversal polydifferential operators of $F$. In particular, for the dg manifold $(T_X^{0,1}[1],\bar{\mathrm{\partial }})$ associated with a complex manifold $X$, we prove that its Hochschild cohomology is canonically isomorphic to the Hochschild cohomology $H{H}^{\bullet }(X)$ of the complex manifold $X$. As an application, we show that the Duflo-Kontsevich type theorem for the dg manifold $(T_X^{0,1}[1],\bar{\mathrm{\partial }})$ implies the Duflo-Kontsevich theorem for complex manifolds.