The pure rotational spectrum of the SrSH radical in its ground electronic ((X) over tilde (2)A') and vibrational states has been measured using millimeter/submillimeter-wave direct absorption techniques. This work is the first observation of SrSH with rotational resolution. The spectrum of its deuterium isotopomer SrSD and SrS (X (1)Sigma (+)) has been recorded as well. These species were created by the reaction of strontium vapor and H2S, in the presence of a dc discharge. SrS was also made with CS2. For SrSH and SrSD, eight rotational transitions were recorded, respectively, for which asymmetry components up to K-a=8 were measured; fine structure was also resolved in each component. Thirteen transitions of SrS in each of its v=0, 1, and 2 states have additionally been observed. These data have been analyzed and spectroscopic parameters determined for all three species, including spin-rotation terms for the strontium hydrosulfides. From an r(0) structure calculation, the bond angle in SrSH was determined to be 91.48(3)degrees, very close to that of H2S and CaSH. This geometry indicates that SrSH is a covalently bonded molecule, as opposed to linear (and ionic) SrOH. The Sr-S bond length in SrSH was also found to be greater than that of SrS (r(Sr-S)=2.705 Angstrom versus 2.441 Angstrom), indicating a change in bond order. In addition, the spin-rotation interaction in SrSH and SrSD includes a small contribution from the off-diagonal term, (epsilon (ab)+epsilon (ba))/2, resulting from the crossing of energy levels with DeltaJ=0, DeltaK(a)=+/-1. Second-order spin-orbit coupling appears to make a significant contribution to the spin-rotation splitting, as well, which must arise from mixing of the (A) over tilde (2)A' and (B) over tilde (2)A" excited states.