Is it necessary to get probate a registered will in Chandigarh.

Hello, My father expired last month. He has left a registered will in my favour for a Chandigarh Housing Board Flat. Will was got registered in the Sub-Registrar Office, Sector 17, Chandigarh during the year 2010. I am the only son and have living mother and three married sisters. Chandigarh Housing Board is not having any problem regarding the transfer of flat in my name on the basis of registered will and has asked me to full fill some documents formalities, one of the required formality is to get a NOC from the Bank where property is mortgaged. I alongwith my father is having a joint Home Loan Bank account in State Bank of India for the above said flat. My father is the main applicant and I am the co-applicant in the loan account since 2007. I have informed SBI regarding the death of my father with death certificate and copy of registered will. I have further intimated them that I have already paid instalment for the month of Aug, 2015 and now onwards I will pay the loan amount instalments and has also requested them to issue NOC so that I can submit the same to Chandigarh Housing Board. But SBI has asked me to first get my registered will probate, then only SBI will issue NOC. Please advise is bank's demand to get the registered will probate is genuine or not?