Yes...you are required to put both W-2 forms in your tax return...ALL income must be reported, even bank interest of 50cents and greater...even if you didn't get a 1099-INT form.
IF you don't put in that W-2, the IRS DOES get copies, and they will end up sending you a letter for what you missed reporting, and charge you the extra taxes PLUS penalties and interest for the months that it went unpaid...It could take them 6-12 months to catch up with you, and the extra interest charges continue to accrue.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
