The closing date is not the important date, that is the date your property was made available for rent. That is the date the property is placed in service. If that was in December of 2020, it would trigger depreciation on the house (not the land). Residential Real Estate uses a mid-year convention, so no matter when during the year you place the property in service, it will have a half year of depreciation expense for the year.
So, if you placed the property in service in 2020, set it up in TurboTax. If you didn't place the property in service until 2021, you don't have anything to do for 2020.
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