The microwave spectra of cyclopropanethiol, C3H5SH, and one deuterated species C3H5SD, have been investigated in the 20 - 80 GHz frequency range. The spectra of the ground vibrational state and of three vibrationally excited states of the parent species of a conformer which has a synclinal ("gauche") arrangement for the H-C-S-H chain of atoms, was assigned. The H-C-S-H dihedral angle is 76(5)degrees from synperiplanar (W). The b-type transitions of the ground and of the vibrationally excited states of the parent species were split into two components, which is assumed to arise from tunneling of the proton of the thiol group between two equivalent synclinal potential wells. No splitting was resolved in the spectrum Of C3H5SD. The tunneling frequency of the ground vibrational state of C3H5SH is 1.664(22) MHz. The tunneling frequency of the first excited-state of the C-S torsion is 52.330(44) MHz, whereas this frequency is 26.43(13) and 3.286(61) MHz, respectively, for the first excited states of the two lowest bending vibrations. The dipole moment of the ground vibrational state of the parent species is mu(a) = 4.09(5), mu(b) = 2.83(11), mu(c) = 0.89(32), and mu(tot)= 5.06(16) x 10(-30) C m. The microwave study has been augmented by high-level density functional and ab initio quantum chemical calculations.