A man who sexually assaulted and killed teenage model Sally Anne Bowman also bit her.
Miss Bowman may have been targeted by a serial attacker
Det Ch Insp Stuart Cundy said he hoped the information would encourage anyone in a relationship with someone they were suspicious of to come forward.
Miss Bowman, 18, was stabbed to death just yards from her home in South Croydon, south London, two months ago.
Police think her attacker may be a serial rapist after tests linked her murder to an attack in Purley in 2001.
It is also thought the man may have attacked a female motorist just hours before Miss Bowman's murder in the early hours of 25 September.
Appealing for information, Det Ch Insp Cundy said: "Are you in a relationship with a man who has bitten you or talked about biting you?
"Have you been in a relationship previously where the man has bitten you? If so, I would strongly urge you to call me.
"I understand that people have loyalties or may even be frightened of someone they are with, but I would like to reassure you that you can call in complete confidence."
The officer in charge of the murder investigation also said any suspect could be eliminated with a simple DNA test.
Police said it is vital they hear from a woman who contacted them on 30 October to say she thought an e-fit of Sally Anne Bowman's killer looked like an ex-boyfriend of hers.
She was too distraught to continue the call and her husband took over.
The murder suspect is described as white, in his 20s or 30s, with short brown hair and is between 5ft 9in and 6ft tall.