  Integrability of a square billiard is spontaneously broken as it rotates
about one of its corners. The system becomes quasi-integrable where the
invariant tori are broken with respect to a certain parameter, $\lambda =
2E/\omega^{2}$ where E is the energy of the particle inside the billiard and
$\omega$ is the angular frequency of rotation of billiard. We study the system
classically and quantum mechanically in view of obtaining a correspondence in
the two descriptions. Classical phase space in Poincar\'{e} surface of section
shows transition from regular to chaotic motion as the parameter $\lambda$ is
decreased. In the Quantum counterpart, the spectral statistics shows a
transition from Poisson to Wigner distribution as the system turns chaotic with
decrease in $\lambda$. The wavefunction statistics however show breakdown of
time-reversal symmetry as $\lambda$ decreases.
