The actor's costar and girlfriend is making "appropriate arrangements" with Monteith's relatives

Lea Michele issued a statement via her reps Tuesday after the coroner announced her boyfriend Cory Monteith died of a mixture of heroin and alcohol.

“Lea is deeply grateful for all the love and support she s received from family, friends, and fans. Since Cory s passing, Lea has been grieving alongside his family and making appropriate arrangements with them,” reads the statement, obtained by PEOPLE exclusively.

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“They are supporting each other as they endure this profound loss together. We continue to ask the media to respect the privacy of Lea and Cory s family.

Monteith, 31, whose body was found in a Vancouver hotel room over the weekend, died in what the coroner called a “most-tragic accident.”

The two stars of Glee dated for more than a year, and Michele, 26, stood by his side when he voluntarily entered a month-long treatment program for substance addiction. They reunited after he was released.