Sorry if this has been posted already. I just find it strange that if she doesn't know anything, and had nothing to hide, then why seek immunity before answering any more questions? Here's a link to the article:
http://news.yahoo.com/s/ap/20080804/ap_on_en_mo/heath_ledger
http://news.yahoo.com/s/ap/20080804/ap_on_en_mo/heath_ledger

until she could get her guard over there (to clear out any evidence of illegal drugs, first.) She might have thought it was a simple overdose. They'll pump out his stomach & be done. But she didn't want Ledger facing jail time if he had illegal drugs scattered around the apartment.