NGC 4258 is an SABbc Seyfert galaxy, located at a distance of 7.2 +/- 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 H2O maser emission allows a very precise measurement of the central supermassive black hole mass (M-circle(maser) = 3.78 +/- 0.01 x 10(7) M-circle dot). 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 FWHMBr gamma (broad) = 1600 +/- 29 km s(-1). The spatial morphology and kinematics of the H-2 gamma 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 H2O 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-circle(broad) = 2.8 +/- 1.0 x 10(7) M-circle dot) is compatible, at 1 sigma level, with the precise measurement resulting from the H2O maser emission.