Can I file my 2015 and 2016 state taxes can I do it here?

If you did not use TurboTax for your 2015 or 2016 federal returns you cannot prepare state returns using TT.  Information flows from the federal return to the state return.  TT cannot be used to prepare "stand alone" state returns.

If you did use TurboTax for those federal returns then you can go back and use the downloaded desktop software to prepare state returns and mail them in.  They cannot be e-filed.

To finish a prior year return started in TT online:https://ttlc.intuit.com/questions/2559403-how-do-i-finish-a-prior-year-return-that-i-started-in-turb

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 and/or your state received the return.

Another option would be to get the forms from your state and prepare them by hand, and then mail them in.  You will need copies of your federal returns for those tax years in front of you in order to prepare the state returns.

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573