Heath Ledger, who plays The Joker in the new Batman film, died in January from an accidental overdose of a cocktail of drugs, including some very powerful painkillers which he didn't have a prescription for.
Heath's masseuse phoned Mary-Kate, who was in California at the time, when she discovered his body. Mary-Kate sent people over to his flat in New York to see if they could help.
Everyone else the police have asked to speak to, including Heather Ledger's ex-girlfriend Michelle Williams, has agreed to answer their questions.
Mary-Kate may not be given immunity and could be served with a subpoena, which would mean she would have to give evidence in front of a jury.
Mary-Kate's lawyers say she has already told the police everything she can and doesn't know where Heath got the drugs from.
Where to next?
Dealing with a teen who takes drugs
Signs of teen drug use
Knowing about drugs