This is quite a recent development. The idea is, on the face of it, ludicrous. One cannot laugh at murder. However, even Shakespeare’s tragedies have their comic relief. 
The crimes in classical mysteries such as those of Agatha Christie were never very real to the reader -deduction was the name of the game. The unravelling of clues and deductions on the basis of character was what we enjoyed. In these less gruesome stories comedy is perfectly appropriate.
Indeed with writers like Elizabeth Peters, one wonders if the murder is really necessary. The situation is comic, as are most of the characters, and one coasts along enjoyably, not really trying very hard to follow the plot. She is well known for her Amelia Peabody series, but some of her earlier books are, I think more agreeably comic and less slapstick. I particularly enjoyed Vicky Bliss. She blossoms in Street of the Five Moons when she meets the slippery, crooked, but very sexy (romance raising its head again) John Smythe.
Another writer who mixes mystery with laughter is Sarah Caudwell, sadly no longer with us. Dramatic irony abounds, the women are the ones who hunt the men, rather than the other way around (sex again), and one is continually erupting into amused giggles which cause stiffly disapproving looks on trains. Her lawyer protagonists are decidedly unstuffy. The best book is, I think, Thus was Adonis Murdered where a young barrister, Julia Larwood, manages to seduce a beautiful young man, only to be the only possible suspect for his murder. Erudite, hilarious, and very tongue in cheek.