We present new spectroscopic and photometric data on the early-type overcontact binary TU Muscae . The analysis of the spectroscopic data shows that the line of sight to the system crosses three kinematically sharp and well-separated interstellar reddening sources and that the stars rotate synchronously . We present new radial velocities that are in good agreement with earlier optical velocities and , thus , do not confirm the systematically smaller velocities obtained from IUE spectra . The optical velocities are analyzed simultaneously with the photometric data to derive accurate absolute dimesions for the binary components.The results show that TU Mus consists of an O7.5 primary with M _ { 1 } = 23.5 \pm 0.8 M _ { \sun } , R _ { 1 } = 7.48 \pm 0.08 R _ { \sun } and an O9.5 secondary with M _ { 2 } = 15.3 \pm 0.4 M _ { \sun } , R _ { 2 } = 6.15 \pm 0.07 R _ { \sun } in an overcontact configuration and that the orbital period has remained constant over the three decades covered by the observations . These results might imply that the mass transfer seen in late-type overcontact binaries does not occur in their early-type counterparts .