I'm rejecting a tenant's application because of his credit report. I do know what that denial letter should look like.
I'm sending his co-applicant a rejection letter too but I'm not sure of the correct legal language to include.
If the application is joint, you're only declining one application, and you're doing that for reason of credit history.
Send the applicants one letter (or each applicant a copy of the same letter) which accords to the law of your jurisdiction, to inform them of the decision and the reason.
If you don't have permission to share personal information between co-applicants, simply say application was declined because co-applicant's was.