We report the results of high spatial and spectral resolution integral-field spectroscopy of the central \sim 3 \times 3 arcsec ^ { 2 } of the active galaxy NGC 1275 ( Perseus A ) , based on observations with the Near-infrared Integral Field Spectrograph ( NIFS ) and the ALTAIR adaptive-optics system on the Gemini North telescope . The circum-nuclear disc in the inner R \sim 50 pc of NGC 1275 is seen in both the H _ { 2 } and [ Fe ii ] lines . The disc is interpreted as the outer part of a collisionally-excited turbulent accretion disc . The kinematic major axis of the disc at a position angle of 68 ^ { \circ } is oriented perpendicular to the radio jet . A streamer-like feature to the south-west of the disc , detected in H _ { 2 } but not in [ Fe ii ] , is discussed as one of possibly several molecular streamers , presumably falling into the nuclear region . Indications of an ionization structure within the disc are deduced from the He i and Br \gamma emission lines , which may partially originate from the inner portions of the accretion disc . The kinematics of these two lines agrees with the signature of the circum-nuclear disc , but both lines display a larger central velocity dispersion than the H _ { 2 } line . The rovibrational H _ { 2 } transitions from the core of NGC 1275 are indicative of thermal excitation caused by shocks and agree with excitation temperatures of \sim 1360 and \sim 4290 K for the lower- and higher-energy H _ { 2 } transitions , respectively . The data suggest X-ray heating as the dominant excitation mechanism of [ Fe ii ] emission in the core , while fast shocks are a possible alternative . The [ Fe ii ] lines indicate an electron density of \sim 4000 \mathrm { cm ^ { -3 } } . The H _ { 2 } disc is modelled using simulated NIFS data cubes of H _ { 2 } emission from inclined discs in Keplerian rotation around a central mass . Assuming a disc inclination of 45 ^ { \circ } \pm 10 ^ { \circ } , the best-fitting models imply a central mass of ( 8 ^ { +7 } _ { -2 } ) \times 10 ^ { 8 } \mathrm { M _ { \odot } } . Taken as a black-hole mass estimate , this value is larger than previous estimates for the black-hole mass in NGC 1275 , but is in agreement with the M - \sigma relation within the rms scatter . However , the molecular gas mass in the core region is tentatively estimated to be non-negligible , which suggests that the central mass may rather represent an upper limit for the black-hole mass . In comparison to other H _ { 2 } -luminous radio galaxies , we discuss the relative role of jet feedback and accretion in driving shocks and turbulence in the molecular gas component .