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You are correct that most closing costs are not tax deductible. Some of the fees associated with the refinance you may be able to include in your basis, but you can not deduct them on your taxes. The deductions of closing costs will vary slightly depending on whether you bought a home or refinanced a home. The only settlement or closing costs you can deduct are home mortgage interest and certain real estate taxes (also points, but you have stated that you did not pay any points so we will not get into that). You deduct them in the year you buy your home if you itemize your deductions. You can add certain other settlement or closing costs to the basis of your home. There are some settlement or closing costs that you cannot deduct or add to the basis.
Below are a couple of links with information regarding what you can deduct, and what you can and can't include in your cost basis.
Below are some of the items that you can and can not add to the basis of your home:
Some of the settlement fees or closing costs that you can include in your basis are:
Abstract fees (abstract of title fees),
Charges for installing utility services,
Legal fees (including fees for the title search and preparing the sales contract and deed),
Transfer or stamp taxes,
Owner's title insurance, and
Any amounts the seller owes that you agree to pay, such as:
Certain real estate taxes (discussed later),
Recording or mortgage fees,
Charges for improvements or repairs, and
Some settlement fees and closing costs you cannot include in your basis are:
Fire insurance premiums,
Rent for occupancy of the house before closing,
Charges for utilities or other services related to occupancy of the house before closing,
Any fee or cost that you deducted as a moving expense (allowed for certain fees and costs before 1994),
Charges connected with getting a mortgage loan, such as:
Mortgage insurance premiums (including funding fees connected with loans guaranteed by the Department of Veterans Affairs),
Loan assumption fees,
Cost of a credit report,
Fee for an appraisal required by a lender, and
Fees for refinancing a mortgage.