If you refinanced with the same lender, then you don't get to deduct the remaining amortized costs from the first loan. Those remaining costs get added to your new loan acquisition cost and that new total gets amortized over the life of the new loan.
If you refinanced with a new lender, then the program "should" automatically adjust your cost basis of your "ORIGINAL" purchase price by adding the remaining amount to be amortized, to that original cost basis. But the key to getting the program to do that, is to enter the 1098 from the "OLD" loan first. Then when you enter the 2nd 1098 (which is from the new loan) *AND* check the box to indicate this is a refi, if the new loan is not from the same lender the program will take care of this for you.
I do not know weather or not the program handles it correctly if the refi is from the same lender, as I've not been through that scenario myself with any of my rentals I've refi'd.
