Microwave rotational spectra for six isotopomers of H2Os(Co)(4) were measured in the 4-12 GHz range using a Flygare-Balle-type spectrometer. The 18 rotational constants from these isotopomers were used to determine eight structural parameters describing the gas-phase structure of this complex. This near-octahedral complex has C-2v symmetry and the dipole moment lies along the c-principal axis for the normal isotopomer. The distance between H atoms, obtained directly from experimental structural parameters, is r(HH) = 2.40(2) Angstrom. This rather long H-H distance indicates that this is clearly a "dihydride" rather than a "dihydrogen" complex. The Os-H bond lengths are r(OsH) = 1.72(1) Angstrom. The osmium-carbonyl carbon bond lengths for axial and equatorial carbonyl groups are ro,cl = 1.96(1) Angstrom and r(OsC3) = 1.97(2) Angstrom. Results for other structural parameters obtained using least-squares fitting and the structural parameters obtained using the Kraitchman method are presented and discussed. No evidence for internal motion was observed for this complex.