We present a new study of the millimeter and submillimeter wave spectra of the thioacetaldehyde molecule, CH3CHS, a sulfur-bearing analog of the ubiquitous interstellar molecule acetaldehyde (CH3CHO). Here, we present a laboratory investigation aimed at determining accurate spectroscopic parameters for CH3CHS to enable astronomical searches for this molecule using radio telescopes at millimeter and submillimeter wavelengths. New laboratory measurements have been carried out between 150 and 660 GHz using the spectrometer of PhLAM in Lille (France). Rotational transitions up to J=60 were assigned in the ground, first, and second excited torsional states of thioacetaldehyde and fit using the RAM Hamiltonian model. The final fit includes 62 parameters to give an overall weighted root-mean-square deviation of 0.9. On the basis of our spectroscopic results, CH3CHS was searched for, but not detected, in data from the Atacama Large Millimeter/submillimeter Array (ALMA) between 84 GHz and 114 GHz toward the hot molecular core Sgr B2(N2). The non-detection implies that thioacetaldehyde is at least 90 times less abundant than acetaldehyde in this source. We also searched for but found no evidence of thioacetaldehyde in a number of prestellar and protostellar sources targeted by the Astrochemical Surveys at IRAM (ASAI) Large Program in nearby low-mass star forming regions.