We present a method to investigate the CP quantum numbers of the Higgs boson in the process e+e− → Zφ at a future e+e− linear collider (LC), where φ, a generic Higgs boson, is a mixture of CP-even and CP-odd states. The procedure consists of a comparison of the data with predictions obtained from Monte Carlo simulations corresponding to the productions of scalar and pseudoscalar Higgs and the interference term which constitutes a distinctive signal of CP violation. We present estimates of the sensitivity of the method from Monte Carlo studies using hypothetical data samples with a full LC detector simulation taking into account the background signals.