We measured the ratio Px/Pz of the transverse to longitudinal components of polarization transferred from electrons to bound protons in C12 by the C12(e→,e′p→) process at the Mainz Microtron (MAMI). We observed consistent deviations from unity of this ratio normalized to the free-proton ratio, (Px/Pz)C12/(Px/Pz)H1, for both s- and p-shell knocked out protons, even though they are embedded in averaged local densities that differ by about a factor of two. The dependence of the double ratio on proton virtuality is similar to the one for knocked out protons from H2 and He4, suggesting a universal behavior. It further implies no dependence on average local nuclear density.