The LL is requesting this information to match it up to the account numbers he will get from the credit report. (Rest assured your account numbers will be on the report he pulls, so he will still have these numbers). If you feel uncomfortable about writing them down, ask if you can just write down the last 4 digits of them so he can still match them up. It will give him enough info to do his job and you won't have given him the entire account numbers. I also ask for these so that a tenant doesn't claim one Visa card when he really has 3. It makes a big difference in his debt to income ratio whether he owes $5,000 to one bill or $15,000 to 3 different accounts.