This is based on reciprocal agreements between Illinois and these states. Employers are expected to withhold state income tax from an employee's wages if that employee is subject to state income tax unless noted below.State agencies should plan to withhold income tax for outofstate workers, since most other states have an income tax. Each state has different tax rules regarding payroll withholding for out-of-state employees. Here's what to know about managing out-of-state employees. You don't owe Illinois state taxes if you work in Washington. I don't know about Washington state taxes. This guide provides information on how state tax reciprocity agreements work and which states currently have agreements in place. Complete Form W-4 so that your employer can withhold the correct federal income tax from your pay. Illinois state income tax withheld from your weekly benefits.