The bodies of 21-year-old Katy Winchester and 26-year-old Kurt Tyrell were found at a house in Tiber Road, North Hykeham, on Sunday, April 3.
Post mortem examinations indicate Winchester was murdered by strangulation by Tyrell, who took his life afterwards by hanging himself.
Winchester was originally from Sleaford and was studying at Manchester Metropolitan University.
Tyrell, who lived on Tiber Road, worked for local electricians Daubney, after going to college in Sleaford and Lincoln.
Lincolnshire Police are not seeking anyone else in connection with the incident.
Further forensic test results are awaited and while a file will be prepared for the local HM Coroner, an inquest into the couple’s deaths will be held.
“The investigation is continuing and we are still speaking to neighbours, associates, families and friends of the deceased couple,” said Det Supt Guy Collings.
“I would like to thank the residents of the estate where this tragedy took place for their patience when experiencing a good deal of inconvenience caused by the road closures and the cordons which we had to implement whilst carrying out our initial investigation.”
Det Supt Collings said the immediate family members of the couple were presently unwilling to release statements to the media and wished to be left in peace to come to terms with the loss.