We present a search for associated production of the chargino and neutralino supersymmetric particles using up to 1.1 fb{-1} of integrated luminosity collected by the CDF II experiment at the Tevatron pp collider at sq rt[s]=1.96 TeV. We analyze events with a large transverse momentum imbalance and either three charged leptons or two charged leptons of the same electric charge. The numbers of observed events are consistent with standard model expectations. Upper limits on the production cross section are derived in different theoretical models.