The shape of emission lines in the optical spectra of star-forming galaxies reveals the kinematics of the diffuse gaseous component. We analyse the shape of prominent emission lines in a sample of $∼$ 53000 star-forming galaxies from the Sloan Digital Sky Survey, focusing on departures from gaussianity. Departures from a single gaussian profile allow us to probe the motion of gas and to assess the role of outflows. The sample is divided into groups according to their stellar velocity dispersion and star formation rate (SFR). The spectra within each group are stacked to improve the signal-to-noise ratio of the emission lines, to remove individual signatures, and to enhance the effect of SFR on the shapes of the emission lines. The moments of the emission lines, including kurtosis and skewness, are determined. We find that most of the emission lines in strong star-forming systems unequivocally feature negative kurtosis. This signature is present in Hβ, Hα, [N II], and [S II] in massive galaxies with high SFRs. We attribute it as evidence of radial outflows of ionised gas driven by the star formation of the galaxies. Also, most of the emission lines in low-mass systems with high SFRs feature negative skewness, and we interpret it as evidence of dust obscuration in the galactic disk. These signatures are however absent in the [O III] line, which is believed to trace a different gas component. The observed trend is significantly stronger in face-on galaxies, indicating that star formation drives the outflows along the galactic rotation axis, presumably the path of least resistance. The data suggest that outflows driven by star formation exert accumulated impacts on the interstellar medium, and the outflow signature is more evident in older galaxies as they have experienced a longer total duration of star formation.