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.
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Cloudy and breezy for much of the day. Rain and stronger winds arriving tonight.
A mostly dry but cloudy morning. Heavy rain and stronger winds this evening.
Another cloudy and breezy day tomorrow. Turning windy with rain arriving tomorrow evening.