2nd baby- rewash all hand-me-downs?

lbw05

This might seem like a silly question, but it just dawned on me. When my son was a baby, I washed everything in dye/perfume-free detergent until his skin wasn't so sensitive anymore and it was determined that regular detergent was fine. As he outgrew the clothes, I had washed them all (in regular detergent) and saved them all in bins. As I prepare for baby #2, and get all the clothes out of storage, do I need to rewash them in dye/perfume-free detergent again? Or is that only recommended for brand new clothes that we might purchase/receive as gifts?

Thanks!