Sarah Libbey Greenhalgh, 48, of Upperville, Va., was found dead early last Monday, July 9, the Fauquier County Sheriff's Office said.
Someone had noticed smoke coming from the residence and called 911. Greenhalgh's body was found inside the home where she lived alone.
Her death was determined to be a homicide but the cause and manner of her death were not publicly released.
The Washington Post said Greenhalgh posted a message on Facebook the night before. She said she was going to sleep with her windows open and hoped "crazy boy left me alone."
Family members said the post referred to a man she had been dating but may have been taken out of context.
Police say they've sought the identity of the man, as well as other men she met through online dating sites. They have also looked at stories she wrote at The Winchester Star newspaper to see if someone might have been angry about something she wrote,
Authorities said they are talking to multiple "persons of interest," The Post reported Friday.
Greenhalgh was from a prominent family. Her late father, William Greenhalgh, served as president of the Montgomery County Board of Supervisors and was once the associate dean of the Georgetown University Law School. Her family's fortune is linked to the founding of Owens Illinois and Libby Owens Ford glassworks.
Celebrity Families of 2014 [PHOTOS]