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Thioformamide NH2CHS is a sulfur-bearing analog of formamide NH2CHO. The latter was detected in the interstellar medium back in the 1970s. Most of the sulfur-containing molecules detected in the interstellar medium are analogs of corresponding oxygen-containing compounds. Therefore, thioformamide is an interesting candidate for a search in the interstellar medium. The rotational spectrum of thioformamide was measured and analyzed in the frequency range 150 to 660 GHz using the Lille spectrometer. We searched for thioformamide toward the high-mass star-forming region Sagittarius (Sgr) B2(N) using the ReMoCA spectral line survey carried out with the Atacama Large Millimeter/submillimeter Array (ALMA). Accurate rotational constants were obtained from the analysis of the ground state of parent, 34S, 13C, and 15N singly substituted isotopic species of thioformamide. For the parent isotopolog, the lowest two excited vibrational states, v12 = 1 and v9 = 1, were analyzed using a model that takes Coriolis coupling into account. Thioformamide was not detected toward the hot cores Sgr B2(N1S) and Sgr B2(N2). The sensitive upper limits indicate that thioformamide is nearly three orders of magnitude at least less abundant than formamide. This is markedly different from methanethiol, which is only about two orders of magnitude less abundant than methanol in both sources. The different behavior shown by methanethiol versus thioformamide may be caused by the preferential formation of the latter (on grains) at late times and low temperatures, when CS abundances are depressed. This reduces the thioformamide-to-formamide ratio, because the HCS radical is not as readily available under these conditions.