Post-mortem examinations are due to be carried out on a man found dead at a Leicester park and his family who were found dead in their home.
Aram Abdul Razaq Aziz, 32, was found at Watermead Country Park on Friday evening.
His former partner Joy Small, 24, his son Aubarr, three, and daughter Chanarra, two, were found on Saturday at a flat two miles away.
Police said they were not looking for anyone in connection with the deaths.
A Leicestershire Police spokesman confirmed police had previously been involved with the couple, and 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 based on the information available the case did not need to be formally referred, but that could change if further information came to light.
A spokesperson from the force said: "No causes of death have been established at present, but 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."
Neighbours expressed their shock at what had happened.
One neighbour, Jennie Bland, 27, described Ms Small as "such a good woman".
She said: "She was a fantastic mum. She would have died for those children."
Floral tributes have been placed outside the flats on Jersey Road along with a pink and blue teddy bear.