We propose an experiment to test the persistence of the polarization in a fusion process, using a terawatt laser hitting a polarized HD target. The polarized protons and deuterons heated in the plasma induced by the laser have a significant probability to fuse producing a 3He and a γ ray or a neutron in the final state. The angular distribution of the radiated γ rays and the change in the corresponding total cross section are related to the polarization persistence, but the resulting signal turns out to be weak. By comparison, the neutrons are produced hadronically with a larger cross section and it is much easier to detect them. A significant reduction of the cross section by parallel polarization of the deuterons as well as a structured angular distribution of the emitted neutrons is reliably predicted by the theory. Therefore, it is expected that the corresponding signal on the neutron counting rate could be seen experimentally.