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The $^{12}$C+$^{12}$C reaction at 95 MeV has been studied through thecomplete charge identification of its products by means of the GARFIELD+RCoexperimental set-up at INFN Laboratori Nazionali di Legnaro (LNL). In thispaper, the first of a series of two, a comparison to a dedicatedHauser-Feshbach calculation allows to select a set of dissipative events whichcorresponds, to a large extent, to the statistical evaporation of highlyexcited $^{24}$Mg. Information on the isotopic distribution of the evaporationresidues in coincidence with their complete evaporation chain is alsoextracted. The set of data puts strong constraints on the behaviour of thelevel density of light nuclei above the threshold for particle emission. Inparticular, a fast increase of the level density parameter with excitationenergy is supported by the data. Residual deviations from a statisticalbehaviour are seen in two specific channels, and tentatively associated with acontamination from direct reactions and/or $\alpha$-clustering effects. Thesechannels are studied in further details in the second paper of the series.

Thermal properties of light nuclei from $^{12}$C+$^{12}$C fusion-evaporation reactions