Measurement of the $D^0\to \phi \eta$, $D^0 \to \omega \eta$ and $D^0 \to K^* \eta$ Branching Fractions

We present updates on the searches for three $D^0 \to V \eta$ decays, where the $D^0$ comes from the decay $D^{*+}\to D^0 \pi^+$ and $V$ is a $\phi$, $\omega$ or $K^*$ vector meson. These results use a 467~fb$^{-1}$ data sample collected with the {\sl B{\scriptsize A}B{\scriptsize AR}} detector at SLAC.