No, if your dependent's only income was $1404 reported on a W-2, then that does not require a tax return. If Federal or state taxes were withheld, then you may want to file a return in order to claim that money back. However, your dependent will need to file their own return. W-2 income of a dependent cannot be included on their parent's return.
To learn more about the filing requirements, take a look at the following TurboTax help article:
Do I need to file my own taxes if I'm a dependent?
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