This is the second part of an Hα kinematics follow-up survey of the Spitzer Infrared Nearby Galaxies Survey (SINGS) sample. The aim of this paper 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 four different telescopes, namely the Canada-France-Hawaii 3.6-m, the ESO La Silla 3.6-m, the William Herschel 4.2-m and the Observatoire du mont Mégantic 1.6-m 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. Based on observations made with the ESO 3.60-m telescope at La Silla Observatories under programme ID 076.B-0859 and on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France and the University of Hawaii. E-mail: isabelle [at] astro.umontreal.ca (isabelle[at]astro[dot]umontreal[dot]ca) (ID);claude.carignan [at] umontreal.ca (claude[dot]carignan[at]umontreal[dot]ca) (CC) ‡ Visiting Astronomer, Canada-France-Hawaii Telescope, operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique de France and the University of Hawaii.