The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest-neighbor spacing distribution P(s) and the spectral rigidity Delta(3)(L) do not follow Poisson statistics. In particular, P(s) shows a sharp peak at s=1 while Delta(3)(L) for small values of L follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.