My 1099-R was issued in 2017 with a code P for 2016 since it was issued before the 4/18/17 tax deadline for 2016 taxes but TurboTax only lists code P as taxable in 2015.

TurboTax is correct.   A 2016 1099-R with a code "P" can only be reported on an amended 2015 tax return since the tax on a returned contribution is taxable in the tax year that the contribution was for, not the year that it is returned.   It does  not matter when the 1099-R was issued or the contribution returned, what matters is when the contribution was made.

[NOTE:  when you enter this in to the 2015 amended software, the code "P" will say "taxable in 2014" - don't be confused by that because the next screen will ask if this is a 2015 or 2016 1099-R.  When you choose "2016" then the year advances by one.   (Code "P" is always one year before the issue year on the 1099-R). ]

https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed

https://ttlc.intuit.com/replies/3288565

Therefore, TurboTax assumes the 1099-R is for 2016 so code "P" states "P-Return of contribution taxable in 2015". However, TurboTax asks on one of the following pages "Look at the year on Form 1099-R. Does it show 2016 or 2017?" If 2017 is selected, the code "P" will automatically be updated to "P-Return of contribution taxable in 2016". Correct?

To confirm, I was issued a 2017 1099-R for "Return of contribution taxable in 2016".

Correct for both questions.  If it is a 2017 1099-R

The text in the drop-down box will not change.  However, 2016 TurboTax will treat as taxable in 2016 a code P Form 1099-R that you identify in the follow-up as being a 2017 Form 1099-R, despite what the drop-down text indicates.

But you said that is a 2016 1099-R that must be reported as a 2016 1099-R in the 2015 amended return.  

Is it a 2016 1099-R or a 2017 1099-R?  - The year of the 1099-R is on the form.

A 2017 1099-R with a code "P" is reported on a 2016 tax return.  A 2016 1099-R with a code "P" is reported on a 2015 tax return.

My original question was confusing - it is a 2017 1099-R with a code "P" to be reported on a 2016 tax return.

I'm all clear now. Thanks!