The purchaser must by Law be a citizen of the state you are selling the gun in (the same state you are a citizen in, no cross state line sales).
Since this is a pistol the purchaser must have (per State Law, this applies to individuals as well as FFL's) either a Firearm (Handgun) Purchase Certificate, Concealed Handgun Permit or Police Credentials that are valid and not expired.
There are communities in Nebraska besides Lincoln that require the seller to report the sale to the local police, Omaha is the only one with a registration requirement that places the duty to the purchaser; so check your local ordinances
For protection of yourself, require a government issued photo ID (great place to check that the purchaser is over 21 as required by law), as well as the Purchase Permit/CHP and record the expiration dates and Number of these items on some form of receipt that the person receiving the pistol signs. For ID to be valid, it needs to have the purchasers current address, a CHP also must have the purchasers current address, the Firearm Purchase Permit does not have that requirement (some businesses have that as part of their policy, for their protection).
If you are uncertain that you are doing things correctly, or just want to make certain that everything is done right you can do the transfer through an FFL who would do the 4473 and make certain that all the ID's are handled correctly for the price of a transfer fee (depending upon dealer anywhere from $15-35). If you or the purchaser covers that fee is something you can negotiate with the buyer.
Now is an important time to be careful with our private sales, the FBI has suspicions of a Terrorist Cell operating in Minnesota. They have been following them all the way to Kansas City (and yes that include excursions into Nebraska) watching for possible attempts to purchase firearms and other materials. So we are being watched as a community and need to be on our toes to make certain we are doing things the right way.
