NO, you cannot e-file anything for 2016. You cannot use the current online software to prepare a 2016 return. Online preparation and e-filing for 2016 is permanently closed. You have to download 2016 software and then print, sign and mail your return. If you already paid for your TurboTax software, you can contact customer support to push a download of the software to you.
To file a return for a prior tax year
Only a 2017 return can be prepared online and e-filed.
If you need to prepare a return for 2014, 2015, or 2016 you can purchase and download desktop software to do it, then print, sign, and mail the return(s)
https://turbotax.intuit.com/personal-taxes/past-years-products/
(if you want to prepare on paper for free: )
PRIOR YEAR FORMS FROM IRS
2016
Form 1040 https://www.irs.gov/pub/irs-prior/f1040--2016.pdf
Form 1040 Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2016.pdf
Form 1040A https://www.irs.gov/pub/irs-pdf/f1040a.pdf
Form 1040AInstructions https://www.irs.gov/pub/irs-prior/i1040a--2016.pdf
Form1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf
Form1040EZ Instructions https://www.irs.gov/pub/irs-pdf/i1040ez.pdf
https://www.irs.gov/filing/where-to-file-paper-tax-returns-with-or-without-a-payment
Remember to prepare your state return as well—if you live in a state that has a state income tax.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS received the return.