We produce an atlas of homogeneously reduced and calibrated low-resolution IRS spectra of the nuclear regions of nearby early-type galaxies (ETGs, i.e. Es and S0s), in order to build a reference sample in the mid-infrared window. From the Spitzer Heritage Archive we extract ETGs in the Revised Shapley-Ames Catalog of Bright Galaxies having an IRS SL and/or LL spectrum. We recover 91 spectra out of 363 galaxies classified as ETGs in the catalogue: 56 E (E0-E6), 8 mixed E/S0+S0/E and 27 S0 (both normal and barred - SB0) plus mixed types SB0/Sa+SB0/SBa. For each galaxy, we provide the fully reduced and calibrated spectrum and the intensity of nebular and molecular emission lines as well as of the polycyclic aromatic hydrocarbons (PAHs) after a template spectrum of a passively evolving ETG has been subtracted. Spectra are classified into five mid-infrared classes, ranging from active galactic nuclei (class-4) and star-forming nuclei (class-3), to transition class-2 (with PAHs) and class-1 (no-PAHs), to passively evolving nuclei (class-0). A demographic study of mid-infrared spectra shows that Es are significantly more passive than S0s: 46(-10)(+11) per cent of Es and 20(-7)(+11) per cent of S0s have a spectrum of class-0. Emission lines are revealed in 64(-6)(+12) per cent of ETGs. The H2S(1) line is found with similar rate in Es (34(-8)(+10) per cent) and in S0s (51(-12)(+15) per cent). PAHs are detected in 47(-7)(+8) per cent of ETGs, but only 9(-3)(+4) per cent have PAH ratios typical of star-forming galaxies. Several indicators, such as peculiar morphologies and kinematics, the irregular shape of dust-lanes, and radio and X-ray properties, suggest that mid-infrared spectral classes are associated with phases of accretion/feedback phenomena occurring in the nuclei of ETGs.
