Summary: We obtain the Dyson-Mehta \(\Delta_3\)-statistics for pseudo-integrable billiards and show that it is non-universal with a universal trend, also that this trend is similar to the one for integrable billiards. We present a formula, based on exact semiclassical calculations and the proliferation law of periodic orbits, which gives rigidity for the entire range of \(L\). To consolidate our theory, we discuss several examples finding complete agreement with the numerical results, and also the underlying fundamental reasons for the non-universality.