The body of 39-year-old Leanne McKie, a serving officer in Greater Manchester Police was found beside a lake at Poynton Park in the early hours of Friday morning.
Cheshire Police were called to Poynton Park at around 3.45am on Friday after reports that a body had been found
A 43-year-old man from Wilmslow has been arrested on suspicion of murder.
He remains in police custody where he is assisting officers with their enquiries.
Detective Inspector Adam Waller said: “Investigations into her death are currently ongoing and we are working hard to establish the full circumstances surrounding the incident.
“We are aware of a number of rumours circulating in relation to the identity of the victim and, whilst formal identification has not year taken place, we do believe that the victim is 39-year-old Leanne McKie, from Wilmslow.