In Minnesota the carry permit has absolutely nothing to do with/in the purchase process for firearms. The buyer will go into the store, provide proper photo ID that establishes residency such as a driver's license or state issued photo ID card and complete the form 4473. The dealer will call NICS (or state provided alternative) for the instant background check. If NICS says proceed, the dealer completes the form 4473 and the buyer walks out of the store with the gun.If you have a carry license, you'll just need that and your ID. The dealer will have you fill out the federal form and send you on your way with your gun. You don't need to do any paperwork prior to going to the store.
In Minnesota you need a buyers permit or a carry permit and than you fill out the 4473