A Moruga housewife heard screaming in an apartment at Princes Town on Monday night was found dead the next day.
Police suspect that Karen Rauseo, 53, was beaten to death.
Rauseo's bloodied body was discovered on the floor of the kitchen.
There were injuries to the woman's face and chest.
A close male relative with whom Rauseo had shared the apartment has been detained by police.
A police report said that Rauseo, of Indian Walk, and the relative, a 53-year-old mason, moved into the ground floor apartment on Monday.
Investigators were told that at around 8 p.m. screams were heard on the premises.
On Tuesday, around 5.45 p.m., police received and a report went to the apartment.
They were told by Rauseo's relative that he left home around 5 a.m. to go to work at Claxton Bay.
He said that he left Rauseo sleeping.
However, upon his return around 5 p.m. he found her lying on the kitchen floor motionless.
Police said there were no signs of forced entry on the premises.
Supt Dhilpaul, ASP Ramdass, Insps Phillip, Victor and Ribero, Sgt Forbes, WPCs Bickram, Charles and George, PC Nelson, Rampersad and others responded.
An autopsy is expected to be done this week to confirm the cause of death.
PC Nelson is continuing investigations.