She walked into Harpers Leisure Centre at Harpenden, Hertfordshire, yesterday morning - 36 hours after vanishing before she was due to take a fitness class.
Ms Grenside, 25, told her family she was abducted, blindfolded, assaulted and driven around by a kidnapper who remained virtually silent throughout her ordeal, her sister Lucy said yesterday.
Police said Ms Grenside was physically unharmed, but too distressed to be questioned immediately and they were keeping 'an open mind'. 'She is suffering severe shock, great distress. We have very few facts and our only witness is Joanna,' Detective Superintendent Ian Whinnett, of Hertfordshire Police, said.
He added that Ms Grenside had no obvious signs of injury. Police were still awaiting the doctor's report following her physical and psychological examination.
Detailed questioning by police would follow, but it would be 'a long and laborious process' which could take a day or two.
He appealed to anyone who was at the leisure centre at about 7pm on Tuesday and in the town centre at about 7am yesterday to come forward.
'As Joanna parked her car, it appears an incident occurred,' Mr Whinnett said. It appeared she may have been abducted but he was keeping 'an open mind'.
At the family's home yesterday, her sister Lucy, 21, said: 'It has been a real ordeal for her - horrible, sinister. We are relieved we have got her home. We can have a Christmas now.' Another sister, Emma, 27, said the family was ecstatic.
Ms Grenside was reported missing by her boyfriend, Dennis Davis, who also works at the leisure centre, when she failed to appear to take her 7pm class on Tuesday.
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