The dealership’s new hire packets should include an authorization to obtain information from references. The dealership can send this signed document to references to show that the applicant has consented to the dealership investigating the applicant’s background.
More importantly, the authorization should contain a release of both your dealership and the former employer for actions in the reference process. In this way, the former employer is comfortable giving complete answers to the questions the dealership may have, and the dealership can be comfortable doing the investigation it wishes to do.