Under Bayes statistical decision framework, this paper addresses statistical modelling and determination of thresholds for speaker verification sj^stems. It is pointed out that speaker-dependent between-speaker score distribution is bi-modal, as opposed to common believe that the distribution is normal. Previous mono-modal modelling of between-speaker score distribution is then extended to bi-modal modelling. For a text-dependent application, experiments are reported which compare verification results with speaker-independent unique threshold, speaker-dependent mono-modal distributions and speaker-dependent bi-modal distributions. It is observed that speaker-dependent thresholds give dramatic error reduction, as compared to unique threshold and that bimodal and mono-modal distribution models give very close verification results. For a 200 speaker database, using 1 sec of test speech, the resulting System resulted in a 0.65% mean verification error.