Thou shall not lie is one of the Ten Commandments. It is NOT a crime to lie to a police officer.

It is a crime to file a false police report OR to cause a report to be filed when it is based on a lie.

It is illegal to lie under oath (perjury).

It is illegal to lie to a Federal Agent when being investigated.

To the OP’s original question, I don’t know how the individual ended up at the police station but YES it is legal for them to ask and YES it is allowed, however, there could be issues come up later.