A loan is never taxable income as long as you pay it back.
Because the house you refinanced is a rental property, deducting the interest on the refinance loan is problematic to say the least. At best, only part of the interest is deductible as a rental expense, that will be the part that is attributable to the original debt on the property before the refinance. For example, if the remaining balance on the mortgage was $50,000 and you refinanced for $100,000, then at most, 50% of the interest is deductible on schedule E as a rental expense. However, if you are audited, you will need to show the IRS a paper trail that proves that the portion of interest you declare as a rental expense can be directly tied to the rental property.
The interest that you pay on the cash out portion of the mortgage will never be deductible under any situation. As a cash out home equity loan, equity interest is not deductible on schedule A as an itemized deduction. Only interest on loans that are used to buy, build, or substantially renovate your personal home may be deducted on schedule A. However, even after you buy a house with that money, that interest is never deductible, because in order to deduct a home mortgage the loan must be secured by the property in question. Since this refinanced loan will not be secured by the house you eventually buy, the interest will never be deductible.
Once you purchase your new primary residence, you might be able to finance or refinance it in such a way that you pay off the equity part of the loan on the rental property and so that the mortgage for the residence is secured by the residence itself. That would make it deductible as a personal itemized deduction on schedule A.
