We present a search for supersymmetric neutrino ν˜ production using the Tevatron pp collision data collected with the CDF II detector and corresponding to an integrated luminosity of 1  fb−1. We focus on the scenarios predicted by the R-parity violating (RPV) supersymmetric models in which sneutrinos decay to two charged leptons of different flavor. With the data consistent with the standard model expectations, we set upper limits on σ(pp→ν˜)×BR(ν˜→eμ,μτ,eτ) and use these results to constrain the RPV couplings as a function of the sneutrino mass.