Study of $B^0 \to \rho^0 K_S^0$ decays

We present preliminary results of a maximum-likelihood analysis of the $B^{0}$ decay to the final states $\rho^{0}K_s^0$ from data corresponding to an integrated on-resonance luminosity of 211 $\rm fb^{-1}$ recorded by the BaBar experiment at the SLAC PEP-II asymmetric-energy $B$ Factory. We measure the total branching fractions and time dependent CP asymmetries.