Complete Form W-4MN so that your employer can withhold the correct Minnesota income tax from your pay. Consider completing a new Form.To complete an enterable form on a computer: Download the Word document to your computer. Open your saved file and select the View tab in the upper left corner. All nonresident alien employees must fill out two W-4 forms at the time of hire, one for Federal withholding and one for State withholding. Minnesota Withholding Tax is state income tax you as an employer must take out of your employees' wages. Employees can view and change federal adjustments and state withholding information using Self Service. How do I fill this out? Complete Form W-4MNP so the financial institution making these distributions can withhold the correct Minnesota income tax. Minnesota Withholding Tax is state income tax you as an employer must take out of your employees' wages.