Points

You can deduct the points you pay for the home refinance over the life of the loan. For example, if you pay $3,000 in points for a 30 year loan, you can deduct $100 per year.

Previously Undeducted Points

If you have refinanced in the past, you can deduct any previously undeducted points at the time of your refinance. For example, if you paid $2,000 in points for your last refinance but only were able to deduct $1,200, you could deduct the remaining $800.

Interest Payments

You can deduct the interest on the amount of the refinance that accrues on the first $500,000 ($1 million for joint filers) of the refinance or the amount of the original mortgage, whichever is lower.

Excess Interest

You can also deduct the interest on the first $50,000 over the original mortgage amount ($100,000 if you are a joint filer) because it will be treated as home equity debt.

Private Mortgage Insurance

If you have to pay for private mortgage insurance (PMI), you possibly can deduct the PMI you pay on the amount of the original mortgage. You can only deduct the PMI if your income does not exceed the annual limits. If you are a single filer you can deduct all of the PMI payments if your adjusted gross income (AGI) does not exceed $50,000 and part of the payments if your AGI is under $54,000. For joint filers, the AGI limit is $100,000 for a full deduction and $109,000 for a partial deduction.

Source:

IRS: Publication 936, Home Mortgage Interest Deduction

Mortgage Q&A: How is PMI Tax Deduction Regulated?