TurboTax will not know anything about your mailed return, and will continue to show “Ready to Mail” on your account. TurboTax will not know that you put your tax return in an envelope and took it to a mailbox. TurboTax does not get updates on mailed (or emailed) returns.
Wait about 4 weeks from when you mail a return and then you can check the status on the IRS site. https://www.irs.gov/refunds
State returns have to be mailed to the state.
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
In the future, if you mail a tax return (or a payment) to the IRS, it is a good idea to use a mailing service that will track it like UPS or certified mail so you will know it was received.
Did you follow the mailing instructions that printed out when you printed your returns for mailing? Did you attach your W-2's and 1099's that showed tax withheld?
Did you print out your state return and look at it carefully before you mailed it? Does it show that you owe anything to the state?
When you printed out your tax returns, the first page in your printout is File by mail instructions which tells you what pages need to be mailed, what needs to be signed and what needs to be enclosed with the tax return.
Your Federal tax return can be tracked at the IRS website Where's my refund?
This TurboTax Help will help you track your state tax return.