  We report on a search for the flavor-changing neutral-current decay D0 \to
{\mu}+ {\mu}- in pp collisions at \surd s = 1.96 TeV using 360 pb-1 of
integrated luminosity collected by the CDF II detector at the Fermilab Tevatron
collider. A displaced vertex trigger selects long-lived D0 candidates in the
{\mu}+ {\mu}-, {\pi}+{\pi}-, and K-{\pi}+ decay modes. We use the
Cabibbo-favored D0 \to K-{\pi}+ channel to optimize the selection criteria in
an unbiased manner, and the kinematically similar D0 \to{\pi}+ {\pi}- channel
for normalization. We set an upper limit on the branching fraction (D0 -->
{\mu}+ {\mu}-) < 2.1 E-7 (3.0 E-7) at the 90% (95%) confidence level.
