We present a detailed study of the shape of the innermost part of the rotation curves of a sample of 29 nearby spiral galaxies, based on high angular and spectral resolution kinematic H alpha Fabry-Perot observations. In particular, we quantify the steepness of the rotation curve by measuring its slope dv(c)(0). We explore the relationship between the inner slope and several galaxy parameters, such as stellar mass, maximum rotational velocity, central surface brightness (mu(0)), bar strength and bulge-to-total ratio. Even with our limited dynamical range, we find a trend for low-mass galaxies to exhibit shallower rotation curve inner slopes than high-mass galaxies, whereas steep inner slopes are found exclusively in high-mass galaxies. This trend may arise from the relationship between the total stellar mass and the mass of the bulge, which are correlated among them. We find a correlation between the inner slope of the rotation curve and the morphological T-type, complementary to the scaling relation between v(c)(0) and mu(0) previously reported in the literature. Although we find that the inner slope increases with the Fourier amplitude A(2) and decreases with the bar torque Q(b), this may arise from the presence of the bulge implicit in both A(2) and Q(b). As previously noted in the literature, the more compact the mass in the central parts of a galaxy (more concretely, the presence of a bulge), the steeper the inner slopes. We conclude that the baryonic matter dominates the dynamics in the central parts of our sample galaxies.