Carsten Tank was married first to Bartha Sophie Leth (d. 1795) from Halden, and secondly to Catherine von Cappelen (1772–1837), sister of Didrich von Cappelen (1761–1828), who was the deputy for Skien to the Norwegian Constituent Assembly at Eidsvoll in 1814 which established the Constitution of Norway.
The Assembly was elected starting in Christiania in February, and was convened to forge the Norwegian Constitution ("Norges Grunnlov").
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He represented Buskerud at the Norwegian Constituent Assembly at Eidsvoll in 1814, together with Frederik Schmidt who was vicar of Eger and Johan Collett who was County Governor of Buskerud.
In 1814 he participated in the Meeting of Notables which preceded the Norwegian Constituent Assembly (however he was not a part of the Constituent Assembly).