A man and a woman whose bodies were found at a semi-detached house died from gunshot wounds, police said.
Nottinghamshire Police said they were not looking for anyone else in connection with the deaths of the 64-year-old man and 31-year-old woman, who were discovered in the West Bridgford area of Nottingham on Thursday.
The pair were a woman and her disabled father, according to reports.
Neighbour Rodrigo Teixeira, 26, told The Sun: "Police told us it's a suicide pact or one killed the other, then themselves."
The two bodies were found during inquiries to identify a woman found dead in the River Trent on April 15. A post-mortem examination found that she drowned.
Formal identification of all three people is yet to take place and detectives are trying to establish if there is a link between the two incidents.
Officers found the two bodies at the address in North Road shortly after 11am and extensive forensic inquiries have been conducted at the scene.
Speaking on Friday, senior investigating officer Det Chief Insp Kate Meynell said: "A team of detectives are working on this inquiry in order to piece together the chain of events leading up to the deaths.
"At this stage I would like to reassure the community that we are not looking for anyone else in connection with the incident."