We consider the circumnuclear regions of star-forming MaNGA galaxies. The spaxels spectra are classified as active-galactic-nucleus-like (AGN-like), H II-region-like (or SF-like), and intermediate (INT) spectra according to their positions on the Baldwin-Phillips-Terlevich (BPT) diagram. There are the following four configurations of the radiation distributions in the circumnuclear regions in (massive) galaxies: (1) AGN+INT, the innermost region of the AGN-like radiation is surrounded by a ring of radiation of the intermediate type; (2) INT, the central area of radiation of the intermediate type; (3) SF+INT, the inner region of the H II-region-like radiation is surrounded by a ring of radiation of the intermediate type; and (4) SF, the central area of the H II-region-like radiation only. The low ionization nuclear emission line regions (LINERs) of configurations 1 and 2 are examined. The spaxel spectra of the LINERs form a sequences on the BPT diagram, that is, they lie along the known AGN-SF mixing line trajectories. The diagnostic line ratios of the spaxels spectra change smoothly with radius, from AGN-like (or INT) line ratios at the galactic center to H II-region-like at larger galactocentric distances. This is in agreement with the paradigm that the LINERs are excited by AGN activity. We found that the AGN and INT radiation in the circumnuclear region is accompanied by an enhanced gas velocity dispersion σ_gas. The radius of the area of the AGN and INT radiation is similar to the radius of the area with enhanced σ_gas, and the central σ_{gas, c} correlates with the luminosity of the AGN+INT area. We assume that the gas velocity dispersion can serve as an indicator of the AGN activity. An appreciable enhancement of σ_{gas, c} was also measured in the SF-type centers of massive galaxies. The values of σ_{gas, c} for the SF-type centers partly overlap with those of the AGN-type centers. This suggests that the manifestation of the circumnuclear region as AGN or as SF on the BPT diagram depends not only on the value of σ_{gas, c} (the level of the AGN activity) but it is also governed by an additional parameter(s). We find that there is a demarcation line between the positions of the AGN-type and SF-type objects on the central gas velocity dispersion – central Hα surface brightness diagram, in the sense that an object with a given value of σ_{gas, c} is an AGN-type only if the central Hα surface brightness is lower than some value.