It's likely always best to disclose the permit first, and then the weapon. Most LE personnel will tell you that; Whether or not your State has a disclosure law.
You mean those guys who are sworn to uphold the law? I'm sorry, but I see those guys as my peers (even my employees in an indirect sense). I respect them and will support them doing their job, but do not fear them or feel compelled to offer them information about myself that they do not need to know or have a right to know under the law.