You need to be a US citizen to carry a US passport.

If she is a legal resident, she can go down to any passport office and obtain a passport. She should also get a Mexican passport. One never knows when a second passport may come in handy. Most terrorists would refrain from killing a Mexican. They wouldn’t hesitate to kill a Mexican with an American passport.

No, no. deopressolibernow is WRONG!.

Being a legal resident doesn’t give her the right to get an American passport. She needs to become a citizen in order to do that.

She should have a Mexican passport. If she doesn’t, then she must get one at a MEXICAN consulate.

With her Mexican passport and her Permanent Resident Card, she will not have any problems coming back to the US.

Remember.. if she has a Permanent Resident Card, aka Green Card or Resident Alien Card (I think this name is no longer used) she is NOT an American citizen. She’s still a Mexican citizen so she needs to get a Mexican passport. Without that, she cannot travel to Mexico or any other country.
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She currently has a Mexican passport and the US Resident Alien Visa. The US Green Card is her travel document permitting entry to US.

Her Mexican passport will work just fine for entering Mexico and if US Immigration decides to be picky she need only present her Mexican passport and proof of Resident Alien status in US (the Green Card)