The body of Adim Baba, 49, was found in a wheelie bin in Essex Close, Luton, on 17 October 2016.
His death was linked to that of Tabussum Winning, 34, found dead at her home in the same road on 10 October.
A man arrested and bailed in connection with the deaths will "face no further action", a police spokesman said.
"Officers are not looking for anyone else in relation to the deaths," he added.
Mr Baba's body was discovered in a bin outside the entrance to the flats. It had been wrapped in cling film and a purple duvet cover.
Bedfordshire Police also confirmed that "the matter has now been passed to the coroner".
An inquest into both deaths has been opened and adjourned. A date for the full inquest has not yet been set.
Police are no longer looking for anybody in what was initially a double murder investigation, where one body was found in a bin.