The Appalachian Trail is pretty safe but no place is immune from crime and also the Appalachian Trail is hard to get help too you if you do need help.
So I would advise bringing along someone with you when hiking the Appalachian Trail or hiking anywhere remote where you cannot easily get help.
If you become injured and need help you would be very unlikely to get help quick enough or maybe not at all depending on where you're located in the Appalachian Trail.
It's always advised to bring along someone when hiking the Appalachian Trail or any other trail just in case something happens.
But you certainly can hike the Appalachian Trail alone at your own risk.