The police aren't going to investigate the case history. If the fiancé agrees that the person requesting the child is the child's father, and cannot point to a legal reason (protective order, order of guardianship, etc.) why dad can be refused custody, I would expect the police to tell the fiancé to give the child to his father.
If the fiancé wants legal rights, he should consider seeking guardianship. He should do that soon, not after Dad shows up with the police or files a court action of his own. The factors ksmom indicates could be raised in guardianship proceedings, but you're right that they have little relevance to a situation in which a dad requests that a third party turn over his child, even if the child was left with the third party by mom.



