My son worked part-time at a restaurant in 2016. Does he need to file taxes even if he is claimed as a dependent in my tax returns? His income was less than $1000.

In many cases, a dependent may need to file a tax return, but your son is well below the filing threshold if all of his income was W-2 wages.

Therefore, your son is not required to file a return but may elect to do so to obtain a refund of his withholding(s).

If your son files his own return with TurboTax Free Edition, he  should check the box Someone else can claim me on their tax return in the personal information section.