Can power of attorney of Mumbai flat be registered in Bangalore?

I don't know correct ans. but question arose is that according to Maharashtra Stamp Act , payment of stamp duty is necessity . Since property is in Maharashtra you need to pay stamp duty and registration fee to Mahrashtra Govt .

Now under circumstances how you can pay that stamp duty to other state Govt . 

Second thing documents are registered where property is situated or in that Dist. So property related document registered in other state may not be correct procedure. 

Additionally two state problem and two state law are required to be studied . 

You can wait for other opinion but in my opinion bit difficult 

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Other option can be  you pay online stamp duty on GRAS website and make necessary paper to Mumbai. 
There is one clause in Maharashtra Stamp Act if document is not properly registered (Sell agreement of flat ) and stamp duty paid properly then that document can be admissibile as evidence in court of law . So payment of proper stamp duty to Govt of Maharashtra signing document may solve problem 

Other opinion also you need to take