I am not sure to see if I submitted state tax return

There are two file options in TurboTax, e-file and file by mail. To view your chosen file method, scroll down the page of Home screen and click Add a State( you are not really adding it, it's just to get you to the menu). Then over to left, click the File tab. If it says "Filed"on the Filed tab page, this means you e-filed your tax return return. If it says "Ready to mail", this means you chose the file by mail option in TurboTax. With the file by mail option, the tax payer is responsible for printing,signing, and mailing the return. What you need to mail and where to send will be listed on your filing instruction page.

Now,  if you chose to e-file your tax return, your status will be either pending, accepted, or rejected. 

Here are the definitions of each:

Pending means simply means that your e-filed return is on its way and that the government hasn't accepted or rejected it yet.

Rejected means the IRS receive but return your tax return becasue there are minor errors that needs to corrected before they can accept it. You will receive a ACTION NEEDED email fromTurboTax if this happens. The email will list the reason for the rejection.

Accepted means your return was received and the basics (such as the correct social security number) seem to be in order.Accepted is like your receipt, letting you know that the government has your tax return and will now view it for errors. So, after the acceptance phase, the IRS will do a deeper search for errors and other issue such as owe debts. If there are no errors and other issues, then the IRS will approve the refund. After the tax refund is approved, IRS will list your direct deposit date on the IRS Where's My Refund? website.

To track your filed federal tax refund:

1. First, check your e-file status to see if your tax return is pending ,accepted, or rejected by IRS. You can begin checking the e-file status 24-48 hours after submission. To check your e-file status, visit this link:https://turbotax.intuit.com/tax-tools/efile-status-lookup/
2. If it has been accepted, then you would wait for the approval from IRS. After the acceptance phase, you can begin tracking your refund at https://sa.www4.irs.gov/irfof/lang/en/irfofgetstatus.jsp The refund process can take up to 21 days. 

To track your state return, please see this TurboTax FAQ, How do I track my state refund?https://ttlc.intuit.com/replies/3300211

Please see these TurboTax FAQs: 

• My return got accepted. What happens next?
•  When will I get my IRS refund?