I received a W2C before filing my 1040 tax return. Should I attach both my original W2 and my W2C when mailing my tax return?

Nio. Just the corrected W-2.

Is there a reason you are not efiling, though?

Depends on the W-2C ... if the corrected form has all the information on it send only that form ... if the corrected form only shows the changes then send both.

Good point.

Yes, thank you.  My w2c was not complete so I submitted both