1099-R shows 2 states in box 13 labeled "State/Payer's state no". Do I enter into Turbo Tax the info in both "first state" boxes and "second state" boxes?

Yes, you enter the information as it appears on the 1099-R into TurboTax.  

 

If you moved during the year that would explain why you would have two different states reported on your 1099-R.

 

Your retirement income is taxable to the state where you reside when you receive the income.

 

If you moved during the year you will need to file part-year resident returns for both states.

 

Multiple States Where to File

I did not live in 2 states. I don’t know why 2 states are shown as MI/ME followed by a single payer number. Maybe I should call the payer and ask why 2 states are shown?

Check with the payer.  They may need to issue a corrected form.

Thanks for the recommendation to call the payer. Turns out that the ME designation (MI/ME-123456) is part of the payer's number! So MI/ME-123456 is to be read as MI for State, and ME-123456 for the State payer's no.