Are prorated property taxes paid at closing on a rental part of basis or a deduction?

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. 

https://www.irs.gov/publications/p530 

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.