The false reporting allegedly stems from Bryant saying his gun was stolen after someone broke into his car.
WAGA reports investigators also suspect Bryant of rape and murder, but he has not been formally charged with those crimes yet.
Morales was last seen July 26 leaving her home on Santa Anna Drive in Norcross. She reportedly texted her mother to say she was on her way home but never made it. Cellphone data showed her last known location was at Oak Loch Trace, and it stayed in that general vicinity until it was either turned off or died.
WXIA-TV reports Gwinnett County Police do not believe Morales and Bryant had a prior relationship. Bryant reportedly lived in Norcross as well, not far from Morales' home.
In a statement, the city of Doraville referred to Bryant as a "now-former police officer," and added, "The City of Doraville and its Police Department are fully cooperating with the Gwinnett Police Department in its investigation of Mr. Bryant. Our prayers rest with the family and friends of Susana Morales and everyone else affected by this tragedy."