  The present work starts by providing a clear identification of correlations
between critical parameters ($T_c$, $P_c$, $\rho_c$) and bulk quantities at
zero temperature of relativistic mean-field models (RMF) presenting third and
fourth order self-interactions in the scalar field $\sigma$. Motivated by the
nonrelativistic version of this RMF model, we show that effective nucleon mass
($M^*$) and incompressibility ($K_o$), at the saturation density, are
correlated with $T_c$, $P_c$, and $\rho_c$, as well as, binding energy and
saturation density itself. We verify agreement of results with previous
theoretical ones regarding different hadronic models. Concerning recent
experimental data of the symmetric nuclear matter critical parameters, our
study allows a prediction of $T_c$, $P_c$ and $\rho_c$ compatible with such
values, by combining them, through the correlations found, with previous
constraints related to $M^*$ and $K_o$. An improved RMF parametrization, that
better agrees with experimental values for $T_c$, is also indicated.
