  In the framework of the connection theory, a contravariant analog of the
Sternberg coupling procedure is developed for studying a natural class of
Poisson structures on fiber bundles, called coupling tensors. We show that
every Poisson structure near a closed symplectic leaf can be realized as a
coupling tensor. Our main result is a geometric criterion for the neighborhood
equivalence between Poisson structures over the same leaf. This criterion gives
a Poisson analog of the relative Darboux theorem due to Weinstein. Within the
category of the algebroids, coupling tensors are introduced on the dual of the
isotropy of a transitive Lie algebroid over a symplectic base. As a basic
application of these results, we show that there is a well defined notion of a
``linearized'' Poisson structure over a symplectic leaf which gives rise to a
natural model for the linearization problem.
