The t t-bar production cross section and top quark mass are measured in proton-proton collisions at sqrt(s) = 7 TeV in a data sample corresponding to an integrated luminosity of 36 inverse picobarns collected by the CMS experiment. The measurements are performed in events with two leptons (electrons or muons) in the final state. Results of the cross section measurement in events with and without b-quark identification are obtained and combined. The measured value is sigma(t t-bar)=168 +/- 18 (stat.) +/- 14 (syst.) +/- 7 (lumi.) pb, consistent with predictions from the standard model. The top quark mass m(top) is reconstructed with two different methods, a full kinematic analysis and a matrix weighting technique. The combination yields a measurement of m(top)=175.5 +/- 4.6 (stat.) +/- 4.6 (syst.) GeV/c^2.