Context. Understanding which stars explode as which type of supernova (SN) is crucial to measure their contribution to the metal production and feedback halting star formation. Most studies of the gas in the environment of SNe are limited by a small sample size (< 10), hampering any statistical conclusions about their nature. Aims. The goal of this paper is to present the first analysis of atomic gas properties at the positions of a statistically significant sample of SNe in order to constrain their nature. Methods. We selected 133 SNe (29 Ia, 77 II, 27 Ib/c) with existing atomic gas data that have exploded in galaxies. In order to test whether SN positions trace enhancements in the atomic gas distribution, as compared to the atomic gas in the whole extent of the host galaxy, we analysed the fraction of pixels on the H I map that are fainter than the pixel in which the SN is located and the fraction of the H I flux contributed by these pixels. We compared these estimates with both theoretical expectations and simulated models. Results. All types of SNe deviate from the completely random distribution. From the three types of SNe, Type II showed the largest offset from the H I distribution, preferring even higher concentrations of atomic gas. This type of SNe deviated also from being proportional to the stellar surface density of the host. The results are, however, complicated by the limits of the survey in size and the uneven resolution of the H I observations. Furthermore, by direct comparison between the three SN types, we observed that the distributions of these populations are still consistent with each other, or in other words, with being drawn from the same underlying distribution. Conclusions. The obtained results fail to ascertain that Ib/c core-collapse SNe, and possibly Type II SNe, are connected with the densest concentrations of atomic gas in their hosts, unlike what has been suggested for GRBs and Ic-BL SNe. Hence, the birth of progenitors of Type II and Ib/c SNe is still consistent with being connected with the current star formation in their hosts, whereas the progenitors of GRBs and Type Ic-BL SNe require more special conditions such as low metallicity to form.