First, as to who should receive the CD:
In rescindable transactions, the closing disclosure must be given separately to each consumer who has the right to rescind. In transactions that are not rescindable, the closing disclosure may be provided to any consumer with primary liability on the obligation.
Second, signatures aren’t required on the CD. For creditors that have a policy of collecting signatures on the CD it is to evidence the disclosure was provided/received by the consumer and in the applicable timeframe. If a signature doesn’t reflect when the consumer was deemed to have received it your file should be documented well enough to show when it was actually provided.
In the situation you gave, there could possibly be an issue if the second set of borrowers had the right to rescind – if your file isn’t well documented as to why there is a discrepancy, it could appear you didn’t provide the disclosures in the required timeframe. Otherwise I don’t think would be a problem. Bottom line – good file documentation is important.