A man is believed to have killed his former partner and two children before taking his own life.
The body of Aram Abdul Razaq Aziz, 32, was found at Watermead Country Park in Leicester on Friday evening.
His former partner Joy Small, 24, was found along with their son Aubarr Aziz, three, and daughter Chanarra, two, at a flat in Jersey Road in the city - around two miles from the park.
Leicestershire Police named the family, while a close friend of Ms Small claimed Aziz was an "abusive monster".
A police spokesman said: "Officers are investigating the circumstances that led to the deaths of all four. No causes of death have been established at present. Post-mortem examinations are due to be held tomorrow.
"The deaths of the woman and children are being treated as suspicious. Inquiries are at an early stage, but officers are not looking for anyone else at this time."
The spokesman confirmed police had previously been involved with the couple but would not give details.
He said discussions had been held with the Independent Police Complaints Commission (IPCC) as to whether the case should be referred to them.
An IPCC spokeswoman said: "The IPCC has had contact from Leicestershire Police but based on the information available at the moment the case does not need to be formally referred.
"Should any further information come to light during the course of inquiries it should be referred to the IPCC as appropriate."