LiOsO3 is a very unusual metallic ferroelectric. This experiment aims to distinguish between two contrasting possibilities for the ground state of this material which can be deduced from some preliminary experiments at PSI. (1) Is the material a superconductor? This would explain the spontaneous magnetic field which sets in at low temperature which would then be due to time-reversal symmetry breaking superconductivity condensing from the metallic state oncooling. (2) Does the material have a magnetic ground state? Then the relaxation would be due to the slowing down of magnetic fluctuations and the development of static magnetic moments. The proposed experiment will distinguish between these two competing explanations.