The statistical properties of the energy levels calculated for the doubly-odd nuclei ⁸⁴Y, ¹²⁴Cs and ¹⁵⁶Tb within the quasiparticle plus axially symmetric rotor model are studied by means of the two standard statistical tests of random-matrix theory, i.e. the distribution function p(s) of the nearest-neighbour level spacings and the spectral rigidity (Δ₃ statistics). We also investigate the Brody distribution function p_B(s) with a single parameter that describes the chaotic degree of the systematic dynamics and the transition behaviour of the spectral fluctuations between Poisson and Gauss orthogonal ensemble limits.