New CIP required?

If we have a customer who believed her information to be hacked, and closed several checking accounts, and then re-opened new accounts simultaneously, would new CIP forms be required?

The person never ceased being your customer so they would not be considered a new customer for CIP. That being said, always take great care with someone claiming to be an ID Theft victim as fraudsters will use social engineering to trick staff into giving away customer information claiming to be a victim when they are actually the crook.