  Context. The determination of the relative frequency of active galactic
nuclei (AGN) versus other spectral classes, for example, HII region-like (HII),
transition objects (TRAN), passive (PAS), and retired (RET), in a complete set
of galaxies in the local Universe is of primary importance to discriminate the
source of ionization in the nuclear region of galaxies. Aims. Here we aim to
provide a spectroscopic characterization of the nuclei of galaxies belonging to
the Herschel Reference Survey (HRS), a volume and magnitude limited sample
representative of the local Universe, which has become a benchmark for local
and high-z studies, for semianalytical models and cosmological simulations. The
comparison between the nuclear spectral classification and the one determined
on the global galactic scale provides information about how galaxy properties
change from the nuclear to the outer regions. Moreover, the extrapolation of
the global star formation (SF) properties from the SDSS fiber spectroscopy
compared to the one computed by Halpha photometry can be useful for testing the
method based on aperture correction for determining the global star formation
rate (SFR) for local galaxies. Methods. By collecting the existing nuclear
spectroscopy available from the literature, complemented with new observations
obtained using the Loiano 1.52m telescope, we analyze the 322 nuclear spectra
of HRS galaxies. Results. Using two diagnostic diagrams (the BPT and the WHAN)
we provide a nuclear and an integrated spectral classification for the HRS
galaxies. Conclusions. We find that the fraction of AGNs increases with stellar
mass, such that at logM > 10.0 M\odot or 66% of the LTGs are AGNs or TRAN.
