Greg Huett, 61, pilot of the Piper single-engine plane, was not a patient at North Mississippi Medical Center-Iuka, where he was transported following the accident, as of Wednesday afternoon.
Seth Rainwater, 33, the passenger in the plane when it crashed, was reported in good condition at NMMC-Tupelo on Wednesday afternoon, according to a hospital spokeswoman.
Officials at the scene of the accident said Rainwater appeared to have received a head wound and possibly other injuries, but those injuries did not appear life-threatening.
Huett was ambulatory at the scene, but was taken by ambulance to the hospital to be checked out.
Federal Aviation Administration investigators arrived in Tishomingo County about 10 a.m. Wednesday, said E-911 Coordinator Ricky Cummings, who escorted them to the scene.
After mapping out and recording data at the site and taking photos, the investigators said they will make a report to the National Transportation Safety Board, which will determine how the case might proceed.
The FAA officials told homeowners Bobby and Cindy Nelson, in whose backyard the plane crashed Tuesday afternoon, that they would be contacted now by the insurers of the plane to discuss removal from their property and other details, Cummings said.