As long as you qualify for both mortgages (refinancing the rental and your new principal residence), you can do so with triggering a capital gain on the rental property until it`s sold even though the extra cash from the refinance is used to purchase your principal residence.
The key is that you are not allowed to deduct the interest on the portion of the refinanced mortgage that is new.
For example, if your current mortgage on your rental property is, say $150,000 and your increase it to $250,000, the interest that is deductible against rental income is 15/25 of the interest. The remaining 10/25 is not deductible.
If I was doing this, I would consider the extra $100,000.00 as part of my personal mortgage.
You could, as another option, sell your investment property, pay the taxes and put as much equity into your principal residence as possible, finance a new rental property (or the existing one, by way of a few transactions) to the maximum allowed by your Bank. This way, you are able to deduct all the interest on the rental property mortgage and reduce your personal (non deductible) mortgage to its maximum. You can also add in a HELOC on your principal residence to allow for future investment opportunities (always ask for money from the bank when you don`t need it).
The cost is that you are paying taxes now. The benefit is the ability to deduct interest. An analysis would be required to see the cost/benefit.
Todd Stokowski, CA