The charge asymmetry in (t\overline{t}) events is measured using dilepton final states produced in pp collisions at the LHC at (\sqrt{s}) = 8 TeV. The data sample, collected with the CMS detector, corresponds to an integrated luminosity of 19.5fb⁻¹. The measurements are performed using events with two oppositely charged leptons (electrons or muons) and two or more jets, where at least one of the jets is identified as originating from a bottom quark. The charge asymmetry is measured from differences in kinematic distributions, unfolded to the parton level, of positively and negatively charged top quarks and leptons. The (t\overline{t}) and leptonic inclusive charge asymmetries are found to be 0.011 ± 0.011 (stat) ± 0.007 (syst) and 0.003 ± 0.006 (stat) ± 0.003 (syst), respectively. These results, as well as charge asymmetry measurements made as a function of the invariant mass, rapidity, and transverse momentum of the (t\overline{t}) system, are in agreement with predictions of the standard model.