We present observations of the singly and doubly deuterated species of thioformaldehyde, HDCS and D₂CS, toward the dark cloud Barnard 1. This is the first detection of D₂CS in space and in dense, cold prestellar regions. Column densities obtained using rotational diagrams and a large velocity gradient model show an extremely high D enhancement in thioformaldehyde in Barnard 1. Although the column density of H₂CS is smaller than that of H₂CO, both species show similar D enhancements in their singly and doubly deuterated species. A chemical model-including multiply deuterated species-has been used in order to interpret the observations. Predicted rotational frequencies from laboratory data for HDCS and D₂CS are significantly in error when compared to the observed frequencies in space. Consequently, we have derived new rotational constants for these two species and for H₂CS and H₂C³⁴S using the observed frequencies in Barnard 1. The new rotational constants allow us to predict the rotational transitions of these species with the accuracy needed for the narrow line emerging from dark clouds. Rotational constants for HDCS and D₂CS have been obtained from the observed transitions in the laboratory and in space.