If you have a Dealership Loan and they have filled out our loan application and a credit report has been pulled, do we still send them a withdrawn letter if the potential customer decides to get financing through the dealership?

Regulation B does NOT require you to sent any type of notice for withdrawals. This may be bank policy, however. I would simply write "withdrawn" and the date on the application and put it with the other Adverse Action Notices.

It is always a good idea to document the fact that the customer withdrew, but, as David points out, you don't have to send the withdrawn customer anything. This is one of the areas where creditors indulge in over-compliance.

There is also the provision in Reg B's adverse action requirements that provides for multiple creditors. 202.9(g). Under that section, you wouldn't have to send the customer a notice even if you had turned them down because they got credit from another creditor in the arrangement.