This is the second part of an H-alpha kinematics follow-up survey of the Spitzer Infrared Nearby Galaxies Survey (SINGS) sample. The aim of this program is to shed new light on the role of baryons and their kinematics and on the dark/luminous matter relation in the star forming regions of galaxies, in relation with studies at other wavelengths. The data for 37 galaxies are presented. The observations were made using Fabry-Perot interferometry with the photon-counting camera FaNTOmM on 4 different telescopes, namely the Canada-France-Hawaii 3.6m, the ESO La Silla 3.6m, the William Herschel 4.2m, and the Observatoire du mont Megantic 1.6m telescopes. The velocity fields are computed using custom IDL routines designed for an optimal use of the data. The kinematical parameters and rotation curves are derived using the GIPSY software. It is shown that non-circular motions associated with galactic bars affect the kinematical parameters fitting and the velocity gradient of the rotation curves. This leads to incorrect determinations of the baryonic and dark matter distributions in the mass models derived from those rotation curves.