The baby girl suspected of being murdered suffered a head injury in the weeks before her death.
Crystal Hall-Hummel, 11 months, died in hospital on Sunday.
Detectives would not reveal the results of a post-mortem but admitted the injury to Crystal's head did form part of their investigation.
Detective Inspector Carwen Hughes, leading the investigation, said: “Crystal had a bump on her head a couple of weeks ago.
“That is a line of inquiry.”
He dismissed reports Crystal's death was a tragic accident, adding: “I am confident this is a murder inquiry.”
A source close to Crystal suggested she had fallen from her bed shortly before her death.
The person, writing on The Argus's website, said: “Well when Crystal fell off her bed you should have taken her to hospital. RIP Crystal. Love you always.”
Referring to this remark a police source said: “That might well have happened,” but refused to elaborate further.
The 26-year-old Worthing man has been arrested on suspicion of murdering Crystal and bailed until June 20.
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