As per Section 32 of the Protection of Women from Domestic Violence Act, 2005, the offence under Section 31 thereof is non-bailable. Therefore, for the purposes of grant of bail, Section 437 of Cr.P.C. will apply. Section 437(1) uses the language:
“…or is brought before a Court other than the High Court or Court of Session, he may be released on bail,…”.
Therefore, a Court presided over by a Magistrate of Second Class would also be “court” within the meaning of this section and for the purposes of grant of bail if he is handling such a case. I have not come across any provision in Cr.P.C. that debars Magistrate of Second Class from granting bail even if he is handling the case. Only restriction imposed on the Magistrate of Second Class is that he cannot grant “police custody” under Section 167 Cr.P.C. unless he is specially empowered in this behalf by the High Court; however, this is not relevant for your question.
Moreover, as per Section 192 of Cr.P.C., the CJM has the power to make over the trial of a case to a competent Magistrate subordinate to him. The punishment for Section 31 of Domestic Violence Act is one year, which a Magistrate of Second Class is empowered to award as per Section 29(3) of Cr.P.C. Though Section 27 of the Domestic Violence Act says that Magistrate of First Class has the competence to try to offence under the Act, I am not commenting about the legality of the order of CJM of making over of the offence under Section 31 of Domestic Violence Act to the Magistrate of Second Class (he might have done it apparently under Section 192 of Cr.P.C.). However, from the limited question of grant of bail, I think once the case has been marked to the Magistrate of Second Class (whether rightly or wrongly), he has the power to grant bail under Section 437 Cr.P.C.