Public Sector banks are a Public Authority (PA) as defined in the RTI Act 2005. You can get any information from them except which can be denied under any sub sections of Sec 8 of the act.
Private Sector banks do not fall under RTI. However, as per Sec 2(f) of the RTI Act:
f) "information" means any material in any form, including records, documents, memos, e-mails, opinions, advices, press releases, circulars, orders, logbooks, contracts, reports, papers, samples, models, data material held in any electronic form and information relating to any private body which can be accessed by a public authority under any other law for the time being in force;
Therefore you can think of asking information related to Private Banks through other PA's which might have "access" to that information.
Just do a search for "bank" or "banks" or "axis bank" and you will get many threads in the forum, on this matter.