Thanks for posting in the Community, @Courtney2019. I'm here to help determine why state and federal taxes were not withheld from an employee's paycheck.
So that I can provide you with the best resources, could you please let me know which version of QuickBooks and payroll that you're using? For example, it would be helpful to know if you're using QuickBooks Online with Enhanced Payroll.
In the meantime, I wanted to reference that state and federal taxes may not be withheld if a check hasn't met the necessary amount for withholding. This is based on factors like the number of allowances/dependents, pay frequency and marital status. For additional insight into this, such as tables for tax calculation, I recommend IRS Publication 15.
I want to ensure that your employee has the correct withholding and will be keeping an eye out for your response. Cheering you to continued success.