Sussex Police said that the 27-year-old man suspected of murdering Shana Grice in Mile Oak on Thursday (25 August) has been released on bail.
The man has been named in some press reports as Mike Lane.
The force also reissued an appeal for any witnesses to come forward to help with the investigation.
In a statement last night Sussex Police said: “A 27-year-old man from Portslade arrested on suspicion of murder has been released on bail until (Thursday) 29 September pending further inquiries.
“It comes after the body of Shana Grice was found by officers at an address in Chrisdory Road, Mile Oak, just before 9.45am on Thursday (25 August).”
Detective Superintendent Jason Taylor said: “This remains an ongoing investigation and has understandably come as a shock to the local community.
“Our thoughts are with Shana Grice’s family and friends and we would ask anyone who saw anything suspicious in the area, no matter how insignificant you may think it was, to get in touch.”
Witnesses are asked to phone Sussex Police on 101, email 101@sussex.pnn.police.uk or call the independent charity Crimestoppers anonymously on 0800 555111.
Sussex Police added: “As previously announced, the death has been notified to the IPCC (Independent Police Complaints Commission) owing to there having been previous police contact with Shana Grice and other people.
“Her family have been informed of this development.
“We await the IPCC’s decision as to how any internal investigation will be conducted.”