Which form must be completed within three days of a new hire for the U.S. Customs and Immigration Service?

The correct form that must be completed within three days of a new hire for the U.S. Customs and Immigration Service is Form I-9. This form verifies the identity and employment authorization of individuals hired for employment in the United States. Employers are required to have new employees fill out this form and provide necessary documentation to confirm their eligibility to work within three days of their start date.

The other forms mentioned serve different purposes. The Form W-4 is used for tax withholding purposes, and while it needs to be completed by employees, it does not have the same time-sensitive requirement as the I-9. Form 19 and Form 1040 pertain to different matters entirely, with Form 19 being less common and more specific to certain contexts, and Form 1040 serving as an annual income tax return form that individuals file with the IRS, which is not related to the hiring process.