  In this paper, we prove weak uniqueness of hypoelliptic stochastic
differential equation with H{\"o}lder drift, with H{\"o}lder exponent strictly
greater than 1/3. We then extend to a weak framework the previous work [CdR12]
where strong uniqueness was proved when the H{\"o}lder exponent is strictly
greater than 2/3. We also show that this result is sharp, by giving a counter
example to weak uniqueness when the H{\"o}lder exponent is just below 1/3. Our
approach is based on martingale problem formulation of Stroock and Varadhan and
is based on smoothing properties of the associated PDE.
