Abstract : We present searches for the rare decay modes D0 to e+e-, D0 to mu+mu- and D0 to e mu in continuum e+e- to cbar c events recorded by the BABAR detector in a data sample that corresponds to an integrated luminosity of 468 f^-1. These decays are highly GIM suppressed but may be enhanced in several extensions of the Standard Model. Our observed event yields are consistent with the expected backgrounds. An excess is seen in the D0 to mu+mu- channel, although the observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman-Cousins method, we set the following 90% confidence level intervals on the branching fractions: B(D0 to e+e-)<1.7 x 10^-7, B(D0 to mu+mu-) within [0.6, 8.1] x 10^-7, and B(D0 to e mu)<3.3 x 10^-7.