technically it can be both. the IRS say that you can only deduct the portion of taxes for the period you own the property so if there's a proration that doesn't match up with the actual period of ownership basis should be adjusted. see the section on deductible real estate taxes - same rules apply to rental and personal residence.
The property taxes are not added to the basis of the property. They are a rental expense to be deducted against rental income. You will see an option for that when you set up the rental in TurboTax, where you enter the rental expenses.
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