From Latin 'dormire' (to sleep) — same root as 'dormitory' and 'dormouse,' named for its six-month hibernation.
Temporarily inactive or in a state of rest; existing but not active or growing.
From Old French 'dormant,' present participle of 'dormir' (to sleep), from Latin 'dormīre' (to sleep, to be inactive), from PIE *drem- (to sleep, to be drowsy). The PIE root *drem- is a specifically sleep-related root, less widespread than some but well attested: Greek 'dramein' is disputed, but Sanskrit 'drāti' (sleeps) and related forms support the reconstruction. Latin 'dormīre' generated 'dormitōrium' (sleeping place — whence 'dormitory'), 'dormītiō' (a sleeping), and
The 'dormouse' gets its name from this root — Anglo-Norman 'dormeus' (sleepy one), because dormice hibernate for up to six months per year. Lewis Carroll's sleepy Dormouse at the Mad Tea Party is behaving exactly as his name predicts. And a 'dormer' window is one that protrudes from a sleeping room