Paris Brown, 17, had her mobile phone seized and was interviewed under caution by Special Branch investigating the material, they said.
The teenager was forced to stand down from her £15,000-a-year-role as Kent Police's youth police and crime commissioner earlier this month following publication of the tweets.
Today it emerged that Paris's lawyers, Olswang, have written to Kent Police Chief Constable Ian Learmonth about the scope and nature of the investigation, including the decision to seize her phone and for Special Branch to quiz her.
More top news
The M20 London bound carriageway has now been reopened to traffic but Operation Stack is expected to remain in place into the weekend.
Friday morning's forecast for the east of the region
Friday morning's forecast for the west of the region