NEUTRON stars are believed to have solid crusts, which may exhibit tectonic activity analogous to earthquakes on Earth. These ’starquakes’ have been invoked to explain several phenomena associated with neutron stars, such as the flashes of low-energy gamma-rays from soft gamma-ray repeaters(1,2) (SGRs), and abrupt changes (’glitches’) observed in the spin periods of some pulsars(3,4). Here we show that SGR events and earthquakes share four distinctive statistical properties : power-law energy distributions, log-symmetric waiting time distributions, strong positive correlations between waiting times of successive events, and weak or no correlations between intensities and waiting times. These statistical similarities, together with the fact that the crustal energy liberated by starquakes is sufficient in principle to fuel the soft gamma-ray flashes, suggest that SGRs are indeed powered by starquakes.