The mystery surrounding Heath Ledger's death deepened yesterday, when it emerged that the actress Mary-Kate Olsen is refusing to co-operate with investigators trying to establish how the Dark Knight star got hold of the powerful painkillers that caused his accidental fatal overdose.

Olsen has twice told Drug Enforcement Administration (DEA) officers that she will only give evidence about Ledger's death if they grant her immunity from any future prosecution. Her lawyer, Michael C Miller, is refusing to grant access to his client without a guarantee of immunity that protects her "constitutional rights".

The actress was a close friend of Ledger, and remains a central figure in the DEA investigation because she was also the first person called by the masseuse who discovered Ledger's body at his apartment in New York's SoHo district. Her initial reaction to his death raised eyebrows. Instead of telephoning the emergency services, she sent her personal bodyguard to the scene; he arrived at Ledger's flat shortly after the first paramedics, at around 3pm on 22 January.

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DEA officials now say that they need to question Olsen to conclude their investigation into Ledger's death.

Although her lawyer said in a statement this week that Olsen had "nothing whatsoever to do with the drugs found in Ledger's home or his body" and did not know where he had obtained them from, he did not elaborate on her reasons for refusing the interview.

"Regarding the government's investigation, at Ms Olsen's request, we have provided the government with relevant information including facts in the chronology of events surrounding Mr Ledger's death and the fact that Ms Olsen does not know the source of the drugs Mr. Ledger consumed," he said.

The revelation has provoked intense speculation about what, if anything, Olsen may be trying to hide. The actress, who with her twin sister Ashley became famous as a teenage star of the television show Full House, was rumoured to be involved in a relationship with Ledger, 28.

Shortly before Ledger's funeral, she released a statement through her publicist, saying: "Heath was a friend. His death is a tragic loss. My thoughts are with his family."

Everyone else connected with Ledger and his death, including his doctors, the masseuse, his housekeepers, and business associates, have voluntarily co-operated with the DEA investigation.

Michelle Williams, who appeared with Ledger in Brokeback Mountain and is the mother of his daughter Matilda, also agreed to be interviewed by officials, according to the New York Post, which revealed details of Olsen's refusal to co-operate. "Ms Williams was extremely nice and cooperative," a DEA source told the newspaper. Another added: "Everyone has been very eager to help, saying what a great guy Heath Ledger was, everyone except Mary-Kate, who has refused to speak."

The authorities have now obtained a subpoena that could force 22-year-old Olsen to appear before a grand jury, should further negotiations with her lawyer fail.

Ledger's death was caused by an accidental drug overdose, according to the official ruling of New York's medical examiner. DEA officials have discovered that all the drugs found in his body were legally obtained from two physicians, with the exception of two painkillers: OxyContin and Vicodin.

They are now "trying to identify the source," of those painkillers, to determine whether they came from a fake prescription or were illegally obtained by other means "Did they come from a dealer, from a friend?" an official asked in the Post. "If he had a bottle from a friend, was it taken by someone else before police responded? That is what is trying to be determined."