QuickBooks Payroll operates strictly by state and IRS regulations to ensure full compliance with tax laws, nurse2. Let me explain further.
Payroll taxes, including state and local withholdings, are determined by both the employee's residence and work location. In this scenario, you can modify the Filing status of your employee's withholding taxes to Do not withhold to ensure compliance with the state where you do need to collect taxes.

Additionally, I suggest consulting your state tax agency for further clarification. Some states maintain reciprocity agreements that can influence tax withholding. I'll add this article for more info: Set up employees and payroll taxes in a new state.
Lastly, here are some articles that can further assist you in managing your payroll processes. These resources will guide you on how to obtain your state account numbers for payroll, update them, and efficiently run, print, and customize payroll reports:
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