My tax returns were accepted but do I physically mail a check?

I got an email for both state and federal that my returns were accepted so that's good news. I just am not sure if TurboTax saved my bank account info to let federal and state authorities to deduct my taxes automatically. I remember filling out the info but then also getting some error that I was not eligible for e-filing for state, but I made some corrections to my return- and I did not get the message and it allowed for e-filing.

 

How do I ensure that I do not have to physically mail a check for taxes I owe for both federal and state--- more importantly state?

 

Thank you