A comparison of the polarization-transfer to a bound proton in quasi-free kinematics to that of elastic scattering off a free proton can provide information on the characteristics of the bound proton. In elastic scattering, the ratio of the transverse (P_x) to longitudinal (P_z) polarization-transfer components is proportional to the electromagnetic form factor ratio G_E/G_M. This provides a direct measurement of the form factor (FF) ratio and eliminates many systematic uncertainties. Extraction of the polarization components (P_x and P_z), even though can be done with larger uncertainties than their ratio, allow to address the impact of different nuclear effects. Such measurements in quasi-elastic scattering off bound protons have been performed at the Mainz Microtron (MAMI) on ²H and ¹²C, with momentum transfer Q² up to 0.65 (GeV/c)², in order to search for possible modifications to the FF ratio for bound protons. We observe that the deviations in the measured ratios P_x/P_z from those of free-proton scattering have a similar dependence on virtuality (off-shellness) for different nuclei, at a wide range of kinematic settings, implying a universal behavior, and that the same mechanism causes the deviations in each type of nucleus. We will present new data and calculations for carbon and present determined confidence intervals on the possible modifications to G_E/G_M in both carbon and deuteron.