We provide a comprehensive census of the near-infrared (NIR, 0.8-2.4um) spectroscopic properties of 102 nearby (z<0.075) active galactic nuclei (AGN), selected in the hard X-ray band (14-195keV) from the Swift-Burst Alert Telescope survey. With the launch of the James Webb Space Telescope, this regime is of increasing importance for dusty and obscured AGN surveys. We measure black hole masses in 68 per cent (69/102) of the sample using broad emission lines (34/102) and/or the velocity dispersion of the CaII triplet or the CO band-heads (46/102). We find that emission-line diagnostics in the NIR are ineffective at identifying bright, nearby AGN galaxies because [FeII] 1.257um/Pa{beta} and H2 2.12um/Br{gamma} identify only 25 per cent (25/102) as AGN with significant overlap with star-forming galaxies and only 20 per cent of Seyfert 2 have detected coronal lines (6/30). We measure the coronal line emission in Seyfert 2 to be weaker than in Seyfert 1 of the same bolometric luminosity suggesting obscuration by the nuclear torus. We find that the correlation between the hard X-ray and the [SiVI] coronal line luminosity is significantly better than with the [OIII]{lambda}5007 luminosity. Finally, we find 3/29 galaxies (10 per cent) that are optically classified as Seyfert 2 show broad emission lines in the NIR. These AGN have the lowest levels of obscuration among the Seyfert 2s in our sample (logN_H_<22.43cm^-2^), and all show signs of galaxy-scale interactions or mergers suggesting that the optical broad emission lines are obscured by host galaxy dust.