The presence of a time-reversal symmetry-breaking field in the hidden order and superconducting states of URu2Si2 has been studied by muon spin relaxation (μSR) spectroscopy. The development of an internal magnetic field has been observed in the hidden order state. Longitudinal-field μSR experiments have shown that the internal magnetic field is static on the time scale of μSR. The presence of both a- and c-axis components of the internal magnetic field at the muon sites was revealed by transverse- field μSR experiments. This is in contrast to the pressure-induced antiferromagnetic state, where the internal magnetic field is parallel to the c-axis. We also found that the muon spin relaxation rate is further enhanced below the superconducting phase transition temperature, indicating further development of the internal magnetic field.