The energy levels of the odd-odd nucleus 84Y are calculated by using the axially symmetric rotor plus quasiparticles model.The two standard statistical tests of Random-Matrix Theory such as the distribution function p(s) of the nearest-neighbor level spacings (NNS) and the spectral rigidity Δ3 are used to explore the statistical properties of the energy levels.By analyzing the properties of p(s) and Δ3 under various conditions, we find that the quasiparticle features mainly affect the statistical properties of the odd-odd nucleus 84Y through the recoil term and the Coriolis force in this theoretical mode, and that the chaotic degree of the energy levels decreases with the decrease of the Fermi energy and the energy-gap parameters.The effect of the recoil term is small while the Coriolis force plays a major role in the spectral structure of 84 Y.