The Hart surname started in various places. (some information from the learning center at Ancestry)
l. English and North German: from a personal name or nickname meaning 'stag', Middle english hert, Middle Low German herte, harte.
2. German: variant spelling of Hardt 1 and 2.
3. Jewish (Ashkenazic): ornamental name or a nickname from German and Yiddish hart 'hard'.
4. Irish: Anglicized form of Gaelic O hAirt 'descendant of Art', a byname meaning 'bear', 'hero'. The English name became established in Ireland in the 17th century.
5. French: from an Old French word meaning 'rope', hence possibly a metonymic occupational name for a rope maker or a hangman.
6. Dutch: nickname from Middle Dutch hart, hert 'hard', 'strong', 'ruthless', 'unruly'.
7. The Hart surname also had it's starts in Great Brittin, Scotland, Wales, and Prussia.
According to the 1990 U.S. census the HART surname appeared at a frequency of 0.054 and was ranked as the 179 name in frequency.