  We solve the local equivalence problem for sub-Riemannian structures on (2n +
1)-dimensional manifolds. We show that two sub-Riemannian structures are
locally equivalent if and only if? their corresponding canonical linear
connections are equivalent. When n = 1, these connections coincide with the
generalized Tanaka-Webster connection of the corresponding contact metric
structure. We show that in dimension > 5, there may not be any contact metric
manifolds associated with a given sub-Riemannian structure.
