Does employer need to complete a new I-9 for a rehired employee?

It depends on company policy and on the completion date of the previous I-9.

Employers must make a policy decision: to use Section 3 of the existing I-9 when possible (doing new I-9s only when legally required) or to skip the analysis and simply do new I-9s for all rehires.

You may use Section 3 of the I-9 (instead of doing a new I-9) if you are rehiring the employee within three years of the date that the previous Form I-9 was completed. (Note that, if the employee previously indicated that she was an alien authorized to work for a limited period, and that period has expired, you will also need to see a List A or C document and must record the document information in Section 3; this is known as reverification. If you are using Section 3 to reverify, you must ensure that you are using the most recent version of the Form I-9, which as of early 2014 reflects a revision date of 03/08/13 and an expiration date of 03/31/2016.)

If it has been more than three years since the original I-9 was completed, you must complete a new I-9, treating the employee as a new hire for I-9 purposes.

For employers who do not feel that the analysis above will be consistently followed throughout the organization, a policy of completing new I-9s for all rehires may be desirable.