Tax Question - Cash out Refi to Payoff Primary Residence

[Chris Kinney]

One of my rental properties is fully paid off while I have around 200K remaining on the mortgage for my primary residence at an interest rate of 3.875% (and I am only 4 years into the term).   I am thinking of doing a cash out refi on the rental to fully payoff my primary residence if it would be advantageous from a tax perspective (given the new tax law's higher standard deduction for schedule A, I may not qualify for itemized for W2 income).  

If I do a cash out refi, am I able to deduct the the mortgage interest from rental income (I am not sure if this is treated differently than interest from a mortgage used as part of a purchase)? If so, I still am not sure whether it makes sense considering that I would need to do the Refi at an interest rate over 5% vs. the 3.875 I have currently (i.e. does potential tax benefit make up for the increase in rate). Even if it is not a savings but close to a wash, I would still consider the refi because it would give me the ability to substantially increase the limits on my existing HELOC.