Most businesses will tell you that they never ask you for your password or your SSN. It sounds like it's a Scam trust me some are so elaborate that they can copy a business website so it looks like the real thing, they've copied major banks logos, same wording everything. Your best bet is to call Paypal customer service, I've only ever dealt with them once and they were very helpful.
They have all your contact info they would/should contact you directly if they need something like that. Be extremely careful with this.