The dependence of the mass accretion rate on the stellar properties is a key constraint for star formation and disk evolution studies. Here we present a study of a sample of stars in the Chamaeleon I star-forming region carried out using spectra taken with the ESO VLT/X-shooter spectrograph. The sample is nearly complete down to stellar masses (M⋆) ~0.1 M⊙ for the young stars still harboring a disk in this region. We derive the stellar and accretion parameters using a self-consistent method to fit the broadband flux-calibrated medium resolution spectrum. The correlation between accretion luminosity to stellar luminosity, and of mass accretion rate to stellar mass in the logarithmic plane yields slopes of 1.9 ± 0.1 and 2.3 ± 0.3, respectively. These slopes and the accretion rates are consistent with previous results in various star-forming regions and with different theoretical frameworks. However, we find that a broken power-law fit, with a steeper slope for stellar luminosity lower than ~0.45 L⊙ and for stellar masses lower than ~0.3 M⊙ is slightly preferred according to different statistical tests, but the single power-law model is not excluded. The steeper relation for lower mass stars can be interpreted as a faster evolution in the past for accretion in disks around these objects, or as different accretion regimes in different stellar mass ranges. Finally, we find two regions on the mass accretion versus stellar mass plane that are empty of objects: one region at high mass accretion rates and low stellar masses, which is related to the steeper dependence of the two parameters we derived. The second region is located just above the observational limits imposed by chromospheric emission, at M⋆ ~ 0.3 − 0.4 M⊙. These are typical masses where photoevaporation is known to be effective. The mass accretion rates of this region are ~10-10M⊙/yr, which is compatible with the value expected for photoevaporation to rapidly dissipate the inner disk.