  We present first measurements of the double ratio of the polarization
transfer components $(P^{\prime}_{\!x} \!/ P^{\prime}_{\!z} )_p/
(P^{\prime}_{\!x} \!/ P^{\prime}_{\!z} )_s$ for knock-out protons from $s$ and
$p$ shells in $^{12}{\rm C}$ measured by the $^{12}{\rm
C}(\vec{e},{e}'\vec{p}\,)$ reaction in quasi-elastic kinematics. The data are
compared to theoretical predictions in relativistic distorted-wave impulse
approximation. Our results show that differences between $s$- and $p$-shell
protons, observed when compared at the same initial momentum (missing momentum)
largely disappear when the comparison is done at the same proton virtuality. We
observe no density-dependent medium modifications for protons from $s$ and $p$
shells with the same virtuality in spite of the large differences in the
respective nuclear densities.
