We study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has mixed phase space structure consisting of two regular regions separated by a chaotic one. We make use of a simple symmetry of the system to separate the eigenstates of the time-evolution operator into two classes in agreement with the Percival classification scheme. We then use a method firstly developed by Bohigas et al. (1990) to evaluate the fractional measure of states belonging to the regular class, and finally present the level spacing statistics for each class. The level spacing distribution of states belonging to the irregular part of the spectra as well as that of the complete set of levels corroborate the Berry-Robnik surmise. We further present a statistical study of the regular levels. The presence of intermediate states-states which belong to neither class as long as R is finite-phase spatially mixed among the set of regular ones, together with the small fractional measure of regular states strongly affects the corresponding level spacing statistics, resulting in a non-negligible deviation from the expected Poisson distribution. We see, however, the remarkable agreement of the irregular level spacing statistics as a direct confirmation of the Berry-Robnik surmise.