I can help share some information about state payroll taxes in QuickBooks.
You can always remove the state taxes if this is not applicable for your employee. Just follow the steps below:
If you need more details about setting up your S-Corp, you can refer to this article: Set up and record S-Corp health insurance.
This should help guide you in the right direction. As always, if you need other references in the future you can visit our site: Help articles for QuickBooks Payroll.
Keep me posted if you have other questions about your state taxes. I'm here to help.