Sister and I were gifted a property 10 years ago......would we each claim 50% of the basis we inherited for capital gains purposes?
First, correct terminology means everything here. There is a vast difference between "gifted" and "inherited". If the property was gifted to you two, then neither you nor your sister inherited anything. As a part of the gift received, you two were also gifted the giver's original cost basis. So if the property was purchased by the giver in say, 1980 for $25K and when gifted to you two it's FMV (Fair Market Value) was say, 100K, then the cost basis for both of you is the giver's purchase price of $25K. If selling the property that cost basis is split between the two of you. But I strongly suspect you have another problem I'm fixing to make you aware of.
Since *YOU* rented it and *YOU* collected all the rental income, *you* paid all the expenses (Property taxes, mortgage interest, insurance, depreciation, etc) what cost basis did *YOU* use for depreciation? This "REALLY MATTERS" big time.
