Your wife does not file Form 8332 with the IRS. She has to sign it and give the signed copy to you. If you e-file your tax return, you fill out Form 8453, attach the signed Form 8332 to Form 8453, and mail it to the IRS. Keep a copy of the signed Form 8332 for your records.

You could make the case that you don’t need that form since she is not giving up any rights to the dependency because she is not filing a return. But to avoid any complications she can send you the signed form. 

 As the non-custodial parent filing your return electronically, you must file Form 8332 with Form 8453, (U.S. Individual Income Tax Transmittal) for an IRS e-file Return. See Form 8453 and its instructions for more details. This must be done within 3 days of your e-filed return being accepted by the IRS.