Retirement tax questions

If the annuity distribution isn't taxable in PA, then why are PA taxes being withheld in the first place?

I assume you do need to file a PA income tax return.  If that's the case then you prepare that income tax return, an income tax return that doesn't include the distribution in taxable income.  Of course you do enter all your other income that needs to be reported to PA and any taxes you've paid, which includes the withholding from the annuity distribution.  The difference between the tax liability based on your taxable income and all taxes you've paid results in either a refund or reduces the amount you need to send in with your income tax return.  In other words, you won't report this annuity distribution but you will report the withholding.  How the math works out in the end is unknown until you finalize your income tax return.

What do you mean by "TurboTax is not doing it"?