Yes, you can file RTI to State Bank of India. It is a Public Sector Banking and Financial Services Statutory Body and comes under the ambit of RTI.
You can file RTI Application to the concerned Bank / Regional Head Office / Corporate Office by making Payment of Rs. 10/- by Demand Draft or Bankers Cheque or IPO in the name of 'State Bank of India' and payable at the centre where CPIO is located.