Q: After a girl has done the sin of masturbation, is it necessary to take a ghusl or wudhu ?
A: This is indeed a digusting and filthy act. One should make sincere and abundant Taubah and Istighfaar for this, with a firm resolve never to commit this again.
As for Ghusl being compulsory or not kindly see below;
According to us Hanafis there are three situations;
1. Ghusl is compulsory when intercourse takes place irrespective whether the woman has an orgasm or not.
2. Ghusl is compulsory on a woman who has experienced nocturnal emission (wet dream) provided she sees a discharge.
3. If a women is fondled or aroused sexually in some way other than the inserting of anything into her private part and experiences an orgasm then ghusl is compulsory if a discharge is seen. If something was inserted (this refers to any object besides sexual intercourse in which ghusl is obligatory irrespective of whether there was an orgasm or not) and she had an orgasm but did not experience a discharge of semen then as a precautionary measure ghusl should be made (Fataawa Raheemiyyah, Vol.4, Page 28).
And Allah Ta'ala Knows Best
M.D. Mangera (Mufti)