Generally, the funds are withdrawn by the state on the payment date you specified if your return has been accepted and they have begun processing it. Sometimes it may take a couple more days on their end. And if that date happens to fall on a weekend or federal holiday, the funds are typically withdrawn the next business day. If you didn't specify a date, April 17th will be the date they withdraw it.
You won't be penalized as long as your return was filed before April 17th and you chose a date before then for the payment. In the meantime, keep an eye on your bank account – if you still don't see the debit 7-10 days after your return has been accepted and date you specified, contact your state tax agency for an update. All processing of returns, refunds and tax payments are handled by the state and/or IRS only, after they have accepted your return.