Status and update report with private sector banks

I want to get a status and update report from HDFC Bank where I've filed multiple complaints in the past.

I know that you can file RTIs with PSU banks to know the status of your complaints (within in the bank.)

But can you do that with private banks like HDFC? (Not ombudsman complaints but those filed with customer care or nodal officers.)

The date at which the complaint was filed, who was assigned the complaint, whom did he transfer the complaint to, the reason for transferring the complaint, etc.

Basically what you see with any RTI application.

I know that you can track your complaint here: https://leads.hdfcbank.com/applications/misc/CST/cstracker.aspx
However none of my complaints show up on this site.