Complete spin-transfer observables for the two lowest ${1}^{+}$ levels in $^{12}\mathrm{C}$ have been studied with incident protons of 500 MeV. Outgoing protons were detected with an energy resolution of 120 keV at laboratory angles of 3.5\ifmmode^\circ\else\textdegree\fi{}, 5.0\ifmmode^\circ\else\textdegree\fi{}, 7.5\ifmmode^\circ\else\textdegree\fi{}, 9.5\ifmmode^\circ\else\textdegree\fi{}, and 12.5\ifmmode^\circ\else\textdegree\fi{}. Angular distributions of differential cross sections, analyzing powers, and the individual spin observables for each ${1}^{+}$ state are recombined into three transverse and one longitudinal partial differential cross section as well as the spin-sum and spin-difference functions. Results are compared with model calculations and electron-scattering data. Information about experimental quantities not accessible in electron scattering is also discussed.