The investigation into the death of Michael Logan began after an ambulance was called to the Orchard Park Estate on Saturday, August 20.
A post mortem examination has been completed, but the cause of the 48-year-old’s death remains unexplained.
Humberside Police said enquiries were ongoing into the circumstances leading to the death of Mr Logan, who lived in Mulcourt on the estate.
The 36-year-old woman was arrested on Thursday and questioned by detectives.
She has now been released on bail while the investigation continues.
Officers were also carrying out house to house calls to establish any details relevant to the enquiry.
Anyone with information relevant to the investigation is asked to call Humberside Police on 101, quoting log number 167 of 20 August 2016.