If you prepared a 2016 LA state return then it is saved with the pdf of your 2016 tax return, and you can print it out and mail it to the state. Your only proof that you paid state tax due is your own bank or credit card record.
If you did not prepare a 2016 Louisiana return it is too late to use TurboTax to prepare any kind of 2016 return. The 2016 software is no longer available. You could get the forms from the state to prepare it by hand and mail in. You will need to be able to look at your 2016 federal return to prepare the state return.
Do you know how to access the account you used for the 2016 return?
Many people have multiple TT accounts and forget how to access them. Log out of the account you are in now.
Account recovery
https://myturbotax.intuit.com/account-recovery/
https://ttlc.intuit.com/questions/1901535-forgot-your-turbotax-online-user-id-or-password
Or did you use the desktop version of TurboTax? If so, the files are on your own hard drive or any backup device you used like a flash drive.
https://ttlc.intuit.com/questions/1901486-how-many-turbotax-accounts-do-i-have
https://ttlc.intuit.com/questions/1901535
https://ttlc.intuit.com/questions/1901659-find-your-tax-data-file-in-mac
https://ttlc.intuit.com/questions/1900721-find-your-tax-data-file-tax-file-in-windows
To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online
If you need to contact the state for 2016 forms:
https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue
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/state received the return.