EXCLUSIVE

Ellen Page claims a crazed fan has been terrorizing her on Twitter -- sending her multiple DEATH THREATS -- and now, she's turned to the LAPD for help.

The LAPD recently sent a search warrant -- obtained by TMZ -- to the micro-blogging site, demanding information regarding two Twitter accounts believed to be associated with an individual bent on killing the actress.

According to the warrant, the two accounts sent Ellen multiple threatening messages back in June -- such as, "I'm going to murder Ellen Page. She's dead."

And, "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."

The tweets have since been removed.

According to the LAPD, the threats also coincided with a creepy telephone call received by the non-profit that organizes the LA Film Festival, where Ellen's new movie "To Rome with Love" premiered on June 14th. The LAPD claims the caller promised to go to the festival and "kill Page."

Obviously that didn't happen -- but the investigation's still ongoing.