  The possible occurrence of highly deformed configurations in the $^{40}$Ca
di-nuclear system formed in the $^{28}$Si + $^{12}$C reaction is investigated
by analyzing the spectra of emitted light charged particles. Both inclusive and
exclusive measurements of the heavy fragments (A $\geq$ 10) and their
associated light charged particles (protons and $\alpha$ particles) have been
made at the IReS Strasbourg {\sc VIVITRON} Tandem facility at bombarding
energies of $E_{lab} (^{28}$Si) = 112 MeV and 180 MeV by using the {\sc ICARE}
charged particle multidetector array. The energy spectra, velocity
distributions, and both in-plane and out-of-plane angular correlations of light
charged particles are compared to statistical-model calculations using a
consistent set of parameters with spin-dependent level densities. The analysis
suggests the onset of large nuclear deformation in $^{40}$Ca at high spin.
