You should be able to download your first state if you have a software edition that includes one state program. For additional states you purchased, here's how to contact TurboTax Support:
Hours are currently 5AM-5PM Pacific (8AM-8PM Eastern) Monday-Friday.
You can use this contact form to get a phone number, or it may schedule a callback.
https://support.turbotax.intuit.com/contact
Windows or Mac? Here are 3 links that might help.
First of all you download the state program from inside the Turbo Tax program after you install the CD. How to download the state program in Windows…..
https://ttlc.intuit.com/questions/1901109-download-turbotax-state-windows
How to download software you bought at Turbo Tax
How do I download the software I purchased at Turb...
If you want to find the download later,
https://ttlc.intuit.com/questions/1901197-find-your-turbotax-for-windows-software-download