Basically, nothing.
You are looking for IRS publication 523 and 936,
https://www.irs.gov/forms-pubs/about-publication-936
https://www.irs.gov/publications/p936
https://www.irs.gov/forms-pubs/about-publication-523
The only costs that are deductible when refinancing a home are mortgage interest. Mortgage interest includes the daily interest you paid to the new bank from the date you signed the loan to the end of the month, even if it is not included on a 1098.
Mortgage interest also includes "points", if you paid them and if you meet certain conditions. However, on a refinance, you can only spread the points out over the life of the loan -- for a 30 year loan (360 months) you can deduct 1/360th of the point for each payment you made in the tax year.
If you had a previous loan and you were also spreading out the points over the life of that loan, and you refinanced with a different bank, you can deduct your remaining points on that loan when you paid it off. However, if you refinanced with the same bank, you must roll those points into the new loan and start the clock all over again.
Other costs, like appraisals, bank attorney fee, and so on, are not deductible. A few costs might add to your cost basis, which may reduce your capital gains when you sell but are not deductible now. Those costs are listed in publication 523.
