Amanda Jayne Hopkins, 55, was found dead at her home in Sidney Street on Sunday, December 17.
A Humberside Police spokesman said: "Amanda’s death is not being treated as suspicious. However, enquiries to trace a next of kin have so far proved unsuccessful.
"We are asking your help to find Amanda’s next of kin. She is known to have connections with Grimsby and Sheffield."
Anyone who knew Amanda or who has information on the whereabouts of her family is asked to contact HM Coroner on 01472 324005.