We report on a search for a dijet resonance in events with only two or three jets and a large imbalance in the total event transverse momentum. This search is sensitive to the possible production of a new particle in association with a W or Z boson, where the boson decays leptonically with one or more neutrinos in the final state. We use the full data set collected by the CDF II detector at the Tevatron collider at a proton-antiproton center-of-mass energy of 1.96 TeV. These data correspond to an integrated luminosity of 9.1 fb−1. We study the invariant mass distribution of the two jets with highest transverse energy. We find good agreement between data and standard model background expectations and measure the combined cross section for WW, WZ, and ZZ production to be 13.8+3.0−2.7 pb. No significant anomalies are observed in the mass spectrum, and 95% credibility level upper limits are set on the production rates of a potential new particle in association with a W or Z boson.