  NGC 4258 is an SABbc Seyfert galaxy, located at a distance of $7.2 \pm 0.3$
Mpc. This object is well known by its nearly edge-on molecular nuclear disc,
located between 0.16 and 0.28 pc from the nucleus, whose H$_2$O maser emission
allows a very precise measurement of the central supermassive black hole mass
($M_{\bullet}(maser) = 3.78 \pm 0.01 \times 10^7$ Mo). We analyse the emission
line properties and the stellar kinematics in a data cube of the central region
of NGC 4258, obtained, in the K band, with the Near-Infrared Integral Field
Spectrograph, at the Gemini-north telescope. The nuclear spectrum, after the
starlight subtraction, shows only the H$_2 \lambda 2.1218$ $\mu$m and
Br$\gamma$ emission lines, the latter having a broad component with
FWHM$_{Br\gamma}(broad) = 1600 \pm 29$ km s$^{-1}$. The spatial morphology and
kinematics of the H$_2 \lambda 2.1218$ $\mu$m line are consistent with a
rotating molecular disc around the supermassive black hole, with an upper limit
for its diameter of 15.7 pc. The inner radio jet in this object is, in
projection, almost perpendicular to the H$_2$ emitting disc detected in this
work, and also to the H$_2$O maser emitting disc. The main features of the maps
of the stellar kinematic parameters are well reproduced by a model of a thin
rotating stellar circular disc. The supermassive black hole mass provided by
this dynamical modelling ($M_{\bullet}(disc) = 2.8 \pm 1.0 \times 10^7$ Mo) is
compatible, at 1$\sigma$ level, with the precise measurement resulting from the
H$_2$O maser emission.
