Is a woman obligated to cover her hair if she is married with a civil marriage to her Jewish husband, but not married with chuppah, kiddushin and has no kesuba?
Answer:
No, the full obligation to cover hair applies specifically after a Torah marriage. Since civil marriage is not generally considered Torah marriage (we have elaborated on this question here) it follows that the full obligation to cover hair will not apply.
Although there are opinions that require hair covering even before marriage in cases of cohabitation, the general custom is not to be stringent in this matter, and there are authorities to rely upon for this situation (see Pischei Teshuvah, Even HaEzer 21 and see also Otzar HaPoskim).
Best wishes.
