The actor was found dead in his Manhattan apartment in the early hours on Saturday 2 November.
The New York Police Department confirmed the news in a statement that said, upon arrival, "officers observed a 60-year-old male, unconscious and unresponsive, fully-clothed, on his couch".
Tarantina was pronounced dead at the scene. An investigation into the cause of his death is ongoing.
A representative told People magazine: "Brian had been ill lately. He was recently in the hospital and was in the process of recuperating from what I believe to be a heart-related issue."
According to TMZ, Tarantina's niece went to check on him around midnight. After discovering him lying unresponsive on his sofa, she called 911.
His latest role was Jackie in The Marvelous Mrs Maisel, for which he won a Screen Actors Guild Award for Best Ensemble in a Comedy Series, in January this year.
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