  In order to verify Percival's conjecture [J. Phys. B 6,L229 (1973)] we study
a planar billiard in its classical and quantum versions. We provide an
evaluation of the nearest-neighbor level-spacing distribution for the Cassini
oval billiard, taking into account relations with classical results. The
statistical behavior of integrable and ergodic systems has been extensively
confirmed numerically, but that is not the case for the transition between
these two extremes. Our system's classical dynamics undergoes a transition from
integrability to chaos by varying a shape parameter. This feature allows us to
investigate the spectral fluctuations, comparing numerical results with
semiclassical predictions founded on Percival's conjecture. We obtain good
$global$ agreement with those predictions, in clear contrast with similar
comparisons for other systems found in the literature. The structure of some
eigenfunctions, displayed in the quantum Poincar\'e section, provides a clear
explanation of the conjecture.
