It depends on the business. If you have anything other than a Sole Proprietorship (i.e. LLC, C-Corp, S-Corp) then your articles of organization/incorporation would have to list that person (regardless if she is the CFO) as a person with the authority to contract on behalf of the business.
Also, regardless, most bankers / lenders will require with anyone with over a 20% interest in the business to provide a personal guarantee.
Your best bet is to talk with your banker - ask them the best way to proceed - then work to make that happen. They want to close the loan just as much as you do.