Police said other the driver admitted drinking. No charges have been field and toxicology reports are pending.
Smith was not impaired or injured, police said.
Browns owners Dee and Jimmy Haslam offered their condolences to Smith, who signed as a free agent with the team last year. He played one season in Cincinnati and three in Jacksonville.
“Words cannot describe the sorrow we feel for Chris following the loss of his girlfriend, Petara,” the Haslams said.
“Our entire organization mourns with Chris, his family and the Cordero family. We will do everything possible to offer them our support, comfort and any resources in this most difficult time.”
Cleveland’s players were told of the accident during a meeting and coach Freddie Kitchens visited Smith at his home.
Smith and Cordero recently celebrated the birth of a daughter, Haven Harris Smith. He had been excused from the team’s exhibition against Indianapolis last month for the baby’s arrival.
Smith played in Sunday’s season-opening loss to Tennessee. The Browns play at the New York Jets on Monday night.