The woman is accused of following the grey Smart car from Mont à la Brune in St Brelade, along Route des Quennevais, the Airport Road, Route de Beaumont to Victoria Avenue between 5 pm and 5.30 pm on Sunday.
The incident allegedly ended with an altercation on the Esplanade.
The suspect was arrested and later released on bail pending further inquiries.
Anyone with information is being asked to phone the States police on 612612 or Crimestoppers on 0800 555 111.
