The Kentuckian rider, who had joined the Superbike circuit last year, went through the windscreen of the car while he was training at Misano Adriatico, suffering severe brain damage and abdominal injuries.
According to the daily Resto del Carlino, the family has written to the 30-year-old Italian man from Morciano who is being investigated for vehicular homicide.
Authorities are currently examining the scene to gauge whether Hayden gave right of way at the intersection where the accident happened.
Hayden died of his injuries at Cesena's Bufalini Hospital on May 22, aged 35.
With ANSA