A better understanding of sulphur chemistry is needed to solve the interstellar sulphur depletion problem. A way to achieve this goal is to study new S-bearing molecules in the laboratory, obtaining accurate rest frequencies for an astronomical search. We focus on dithioformic acid, HCSSH, which is the sulphur analogue of formic acid. The aim of this study is to provide an accurate line list of the two HCSSH $trans$ and $cis$ isomers in their electronic ground state and a comprehensive centrifugal distortion analysis with an extension of measurements in the millimetre and submillimetre range. We studied the two isomers in the laboratory using an absorption spectrometer employing the frequency-modulation technique. The molecules were produced directly within a free-space cell by glow discharge of a gas mixture. We measured lines belonging to the electronic ground state up to 478 GHz, with a total number of 204 and 139 new rotational transitions, respectively, for $trans$ and $cis$ isomers. The final dataset also includes lines in the centimetre range available from literature. The extension of the measurements in the mm and submm range lead to an accurate set of rotational and centrifugal distortion parameters. This allows us to predict frequencies with estimated uncertainties as low as 5 kHz at 1 mm wavelength. Hence, the new dataset provided by this study can be used for astronomical search.
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