Murphy's house was held in trust, and Monjack is not listed on the title, according to TMZ.com
Executing a will involves signing it in the presence of witnesses and having it notarized. Wills can be amended after they are executed, but it's not clear whether or not Murphy revised hers after marrying Monjack in May 2007.
Murphy, 32, died of cardiac arrest on Sunday. Her mother found her collapsed in the bathroom and called 911. The death is under investigation by the Los Angeles County Coroner's Office. Autopsy results are pending. Foul play is not suspected.
Monjack told PEOPLE in an interview that Murphy did not overdose on drugs and did not suffer from an eating disorder.