The refinance has nothing to do with determining basis. To exclude any gain, you must have lived in the house 2 out of the five years prior to the sale.
When
you converted the property from personal use to rental, the basis for depreciation was lower
of the Adjusted Basis or the FMV on the date of conversion.
Now
that you are selling, it gets a little trickier.
Calculating
Gain/Loss on Subsequent Sale of Rental Property
If a
residence converted to rental property is later sold at a gain, the basis in the converted property is the original cost or other basis plus amounts paid for
capital improvements, less any depreciation taken.
If the sale results in a loss, however, the starting
point for basis is the lower of the property’s adjusted cost basis or FMV when
it was converted from personal to rental property (Regs. Sec.
1.165-9(b)(2)). This rule is designed to ensure that any decline in value
occurring while the property was held as a personal residence does not later
become deductible on the sale of the rental property
