'Only Murders in the Building' Production Not Impacted After Martin Short's Daughter’s Death

Martin Short's recent family tragedy is not impacting production on "Only Murders in the Building" ... TMZ has learned.

Production sources tell TMZ ... the hit Hulu series is not currently in production. We're told typically, if filming were taking place in the United States, the cast and crew would be gearing up to start around this time. However, because the upcoming season is set to film in London, our sources say production isn't scheduled to begin for a couple more months.

We're told no production schedules have been affected following the death of Short's daughter, Katherine Short.

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

Short understandably didn't attend the Actor Awards Sunday, where he 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."