Is credit card debt a open account or is it a written agreement?

Are you looking at your credit report and see a heading called "Open Account"? If that is what you are referring too, it has nothing to do with a written agreement. The credit reporting agencies classify the accounts as either installment, revolving, mortgage or open accounts. Under "open accounts" you may find listed utility companies such as Verizon, student loans, child support, lines of credit or home equity loans. It has nothing to do as to whether the account is open or closed, it is just a classification.