Depreciation is based on the lower of (1) Adjusted Cost B...

In 2016 I have a rental property. For depreciation do I use my original settlement information (2009) or my refinance information (2010)?

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Depreciation is based on the lower of (1) Adjusted Cost Basis, or (2) Fair Market Value at date of conversion to a rental.

Adjusted Cost Basis is usually your (1) original purchase price, plus (2) cost of improvements, minus (3) any depreciation taken prior to conversion to a rental.

In other words, a refinance does not affect it. If it was refinanced while it was a rental, some of the refinance closing costs may be deductible or amortizable.