  We study the weak approximation error of a skew diffusion with bounded
measurable drift and H\"older diffusion coefficient by an Euler-type scheme,
which consists of iteratively simulating skew Brownian motions with constant
drift. We first establish two sided Gaussian bounds for the density of this
approximation scheme. Then, a bound for the difference between the densities of
the skew diffusion and its Euler approximation is obtained. Notably, the weak
approximation error is shown to be of order $h^{\eta/2}$, where $h$ is the time
step of the scheme, $\eta$ being the H\"older exponent of the diffusion
coefficient.
