If you mailed your state, choose your state here https://ttlc.intuit.com/questions/1899433 and it will provide you instructions on how to check the status of your state return on your state's website. You will also find their contact information there.
TurboTax only receives notification that your return was accepted if it was e-filed. Keep an eye on your status and the State will update the information on their site once it is available.