Studies of the spin and parity quantum numbers of the Higgs boson in the WW∗→eνμν final state are presented, based on proton–proton collision data collected by the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 20.3 fb -1 at a centre-of-mass energy of s=8 TeV. The Standard Model spin-parity JCP=0++ hypothesis is compared with alternative hypotheses for both spin and CP. The case where the observed resonance is a mixture of the Standard-Model-like Higgs boson and CP-even ( JCP=0++ ) or CP-odd ( JCP=0+- ) Higgs boson in scenarios beyond the Standard Model is also studied. The data are found to be consistent with the Standard Model prediction and limits are placed on alternative spin and CP hypotheses, including CP mixing in different scenarios.