  We report a search for the decay $B^0 \to J/\psi \phi$, using a sample of 657
$\times 10^6$ $B\bar{B}$ pairs collected with the Belle detector at the
$\Upsilon(4S)$ resonance. No statistically significant signal is found and an
upper limit for the branching fraction is determined to be $\mathcal{B}(B^0 \to
J/\psi \phi) < 9.4 \times 10^{-7}$ at 90% confidence level.
