  We present the first measurement of polarization and CP-violating asymmetries
in $B_s^0$ decays into two light vector mesons, $B_s^0 \to \phi\phi$, and an
improved determination of its branching ratio using 295 decays reconstructed in
a data sample corresponding to 2.9 fb^-1 of integrated luminosity collected by
the CDF experiment at the Fermilab Tevatron collider. The fraction of
longitudinal polarization is determined to be $\fL = 0.348 \pm 0.041 ({\rm
stat}) \pm 0.021 ({\rm syst})$, and the branching ratio $BR ($B_s^0 \to
\phi\phi$) = [2.32 \pm 0.18 ({\rm stat}) \pm 0.82 ({\rm syst})] \times
10^{-5}$. Asymmetries of decay angle distributions sensitive to \CP\ violation
are measured to be $ A_u = - 0.007 \pm 0.064 \stat \pm 0.018 \syst$ and $ A_v =
-0.120 \pm 0.064 \ stat \pm 0.016\syst$.
