Martin Short had a difficult last week ... and decided it was best if he didn't attend the Actors Awards Sunday.

The veteran actor was up for the Outstanding Performance by a Male Actor in a Comedy Series -- an award he won last year -- for "Only Murders in the Building ... but, he was the only one of the five nominees not at the ceremony in Los Angeles.

Seth Rogen ended up taking the trophy anyway ... but, it seems clear Martin skipped the ceremony because his daughter, Katherine, passed away last week.

We broke the story ... Short's daughter died by self-inflicted gunshot wound, law enforcement sources told us. She previously revealed she suffered from mental health issues.

We spoke with a friend who remembered her as a "beautiful empathetic soul" ... who said there were no indications that Katherine was suffering as she was.

She was found behind a locked door ... and a note was found at the scene.

Short had several comedy shows scheduled for this weekend ... but, he postponed those shortly after Katherine was found dead.

She was 42.

RIP

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