So far I know that working in riba-based bank is not allowed. But for central bank, which does not provide loans nor keep deposits based on interest, will it be permissible to work on the central bank (Central Bank of BD -Bangladesh Bank)?.
(I have edited my answer to be more respectful)
The central bank gives loans to private banks and government through the purchase of bonds (on which there is an interest charge). It also allows private banks to deposit money with it overnight for a small interest payment. It essentially does this to create and manage the money supply. Ultimately all money is interest based.
I believe central banks in Muslim majority countries in which sharia takes precedence they use a profit or a rental rate. That might be acceptable if you think Islamic banking is halal. I do not have a reference for that. However Bangladesh's central bank, as far I know, does not operate in that way.
Where does money come from? by J. Collins, T. Greenham, R. Werner and A. Jackson
If you believe that the interest-riba equation holds, then working for the central bank would be religiously unacceptable