A dealer does the preliminary check of the customer's credit history using one of he three credit reporting agencies. This is done to check the customers credit history - whether the customer had any serious credit problems in the past. If any problem is found then the transaction would be terminated.
The bank or the finance company ill do their own enquiry regarding the customer's credit worthiness. The bank or financing company looks for the credit score and the debt-to-income ratio. This credit check is much more detailed than what the dealers would do.