Your situation sets off all kinds of alarms in my head. I cannot imagine any legitimate law enforcement officer making repeated telephone contacts without (1) positively identifying themselves (that is, their name and law enforcement agency they are with) and, (2) following the call up with a personal visit.
My opinion is to reaffirm what Mystic Wave has told you, AND,
- if you have caller ID, make note of the number this person is calling from and share that information with your local law enforcement.
- listen for any "background sounds" when this person calls. Those sounds could help law enforcement identify who this person could be and where they might be calling from.
- do not engage this person in any unnecessary conversation.
- do not share any personal information with this person.
Based on the information you have shared, I conclude the person calling is NOT a law enforcement officer at all - this opens a tremendously dangerous potential for (1) who this person could be and (2) what their intentions might be.