Your son would need to file taxes separately - he especially wants to file himself if he had federal income tax withholding taken out of his check and was due a refund. The real question is if he qualifies as a dependent for you and whether it is better for you to take the dependent deduction on your return or he takes it himself on his. If you are in a higher tax bracket (e.g. your son is still in High School making min wage, but you make decent money), then you likely will pay less taxes overall between you if you take him as a dependent.
Turbotax makes it pretty easy to run the scenario both ways for each of you. I had this situation for my son. In High School and when he first started his career - the first partial year he worked - I took him as a dependent to save taxes, but paid him the amount extra he had to pay by not taking himself as a deduction. After that he no longer lived at home, so the choice wasn't there.
