We present a search for ZZ and ZW vector boson pair production in pp¯ collisions at s√=1.96  TeV using the leptonic decay channels ZZ→llνν, ZZ→lll′l′, and ZW→lll′ν. In a data sample corresponding to an integrated luminosity of 194  pb−1 collected with the Collider Detector at Fermilab, 3 candidate events are found with an expected background of 1.0±0.2 events. We set a 95% confidence level upper limit of 15.2 pb on the cross section for ZZ plus ZW production, compared to the standard model prediction of 5.0±0.4  pb.