  We report the results of a search for the decay B^0 -> e^+ e^-, mu^+ mu^- and
e^{+-} mu^{-+} based on an analysis of 78 fb^{-1} of data collected by the
Belle detector at KEKB. No candidate events have been found. Upper limits on
the branching fractions are calculated at the 90% confidence level: B(B^0 ->
e^+ e^-) < 1.9 x 10^{-7}, B(B^0 -> mu^+ mu^-) < 1.6 x 10^{-7}, and B(B^0 ->
e^{+-} mu^{-+})< 1.7 x 10^{-7}. A limit on the Pati-Salam leptoquark mass
M_{LQ}> 46 TeV/c^2 is obtained at the 90% confidence level.
