We present a new measurement of the inclusive forward-backward tt̅ production asymmetry and its rapidity and mass dependence. The measurements are performed with data corresponding to an integrated luminosity of 5.3  fb-1 of pp̅ collisions at √s=1.96  TeV, recorded with the CDF-II Detector at the Fermilab Tevatron. Significant inclusive asymmetries are observed in both the laboratory frame and the tt̅ rest frame, and in both cases are found to be consistent with CP conservation under interchange of t and t̅ . In the tt̅ rest frame, the asymmetry is observed to increase with the tt̅ rapidity difference, Δy, and with the invariant mass Mtt̅ of the tt̅ system. Fully corrected parton-level asymmetries are derived in two regions of each variable, and the asymmetry is found to be most significant at large Δy and Mtt̅ . For Mtt̅ ≥450  GeV/c2, the parton-level asymmetry in the tt̅ rest frame is Att̅ =0.475±0.114 compared to a next-to-leading order QCD prediction of 0.088±0.013.