If Higgs spin is 1, there is no gg->H production and no H->γγ decay.
For the CP analysis, the golden channel is H->ZZ. The variables most sensitive to CP are the angles (θ1 and θ2) between lepton (distinguished from anti-lepton) and Z direction boosted in the Z rest frame, and the angle (φ) between the decay planes of the two Z's in the H rest frame.
In the SM (CP=+1 for H), in the limit M(H)>>M(Z), the θ distribution goes like sin2θ, i.e. mostly perpendicular to the Z direction. For CP=-1, it goes like 1+cos2θ, i.e. enhanced in the direction parallel to the Z direction.
Reason: in the SM, the heavy Higgs (heavier than 2Z's) mainly decays into longitudinally polarised vector bosons, so the cross section should have a maximum around cosθ=0.
For what concerns φ, the SM predicts 1+βcos 2φ.