In a recent article, Cattaneo, Felder and Tomassini explained how the notion of formality can be used to construct flat Fedosov connections on formal vector bundles on a Poisson manifold M and thus a star product on M through the original Fedosov method for symplectic manifolds. In this paper, we suppose that M is a fibre bundle manifold equipped with a Poisson tensor tangential to the fibers. We show that in this case the construction of Cattaneo-Felder-Tomassini gives tangential star products.