The case has been reopened after Sweeney's family refused to believe that she died of drug overdose, as stated by the Goa Police earlier.
A senior police official here said that registration of murder case last week was a precursor to CBI taking it over.
"CBI does not accept the case, if it is (simply) a case of unnatural death," the official said.
Director General of Police Kishen Kumar refused to comment on the matter.
Sweeney (34) was found unconscious at a night club at Anjuna on April 14, 2010. She died at a private hospital subsequently.
At the time, police said it was a case of drug overdose, but her family alleged foul play.
Her sister, Maureen, claimed there were 20 bruise marks on the body, and autopsy report of the coroner in UK had ruled out traces of alcohol or drugs.