Police have been granted more time to question two men who were earlier arrested near Stone's home in east Devon on suspicion of planning a burglary and having an offensive weapon.
The 24-year-old's spokesperson said that the singer is "getting on with life as normal" following the announcements this morning, The Guardian reports.
Stone's neighbour, farmer Simon Alsop, 57, said: "She came here for a coffee on Tuesday afternoon and she was all right. She was quite laid-back and not in a major panic."
Detective Inspector Steve Parker, who is leading the investigation, said: "The two men in custody had in their possession information relating to an individual in the Cullompton area and items which lead us to suspect that they may have intended to commit a criminal offence.
"Police inquiries continue and the men remain in custody. We're unable to say any more at this time but I would like to thank the local residents for reporting the suspicious car."
He added: "Our officers are currently carrying out reassurance patrols and it's important to stress no properties have been burgled and no individuals have been harmed."
Grammy and Brit Award winner Stone recently unveiled new single 'Somehow', which will feature on her fifth studio album LP1.