It depends.
If you refinanced with the same lender, then the remaining amortized costs not yet deducted on the old mortgage are added to the amortized cost of the new mortgage and amortization starts anew over the life of the new loan.
If you refinanced with a different lender then the remaining amortized costs on the old loan are fully deductible. Then amortized costs on the new loan are entered as such and deducted over the life of the new loan.
