Authorities reportedly are investigating death threats that were sent via Twitter against "Juno" actress Ellen Page.

"I'm going to murder Ellen Page. She's dead," one message read, according to the gossip website TMZ.

"Ellen Page if you continue to date Alexander [Skarsgard] I will K-1-L-L you in public in the next year … Be it in a club, at a game, in a restaurant, or when you're signing autographs," read another, the site reports.

Page, 20, who was nominated for an Oscar for her role in "Juno" and who also starred in the movie "Inception," was spotted with Skarsgard, at a hockey game in Los Angeles last month. The actor stars in HBO's "True Blood."

TMZ claims the threatening messages were sent from two accounts and the Los Angeles Police Department has sent a search warrant to Twitter for information about the accounts.

The tweets reportedly have been removed.

Page has more than 300,000 followers on Twitter, where she describes herself as a "tiny Canadian."

"The Internet makes it easier with YouTube, with Twitter, because these stalkers believe that the celebrities are actually talking directly to them," Rhonda Saunders, a Los Angeles County assistant district attorney who specializes in stalking cases told ABC News. "They think that they have a relationship."

The LAPD said the messages coincided with a phone call to organizers of the L.A. Film Festival, where Page's new movie, "To Rome with Love" premiered June 14, TMZ said. Police said the caller promised to attend the festival and "kill Page."

Page did not attend the movie's premier at the festival.