  Supersymmetric contributions to time independent asymmetry in $B^0_s \to
J/\psi \phi$ process are analyzed in the view of the recent Tevatron
experimental measurements. We show that the experimental limits of the mass
difference $\Delta M_{B_s}$ and the mercury EDM significantly constrain the
SUSY contribution to $B^0_s -\bar{B}^0_s$ mixing, so that $\sin 2 \beta_s \lsim
0.1$. We also point out that the one loop SUSY contribution to $B^0_s \to
J/\psi \phi$ decay can be important and can lead to large indirect CP
asymmetries which are different for different polarization states. These new
physics effects in the decay amplitude can be consistent with CP measurements
in the $B_d$ system.
