SCOTUS has ruled that asking a felon if he is a felon, with regard to gun possession, is a violation of his 5th Amendment rights.
Any charge resulting from such an egregious fishing expedition would rightfully be dismissed.
Citation please. That doesn't pass the smell test. The police are authorized to ask you anything they want. You can simply refuse to answer by invoking your 5th Amendment rights, but there is no prohibition against them asking you damned near anything up until the point you ask for a lawyer to be present or take the 5th.