Vote out of the list offered: 'Bringing up Baby' - Cary Grant did screwball better than anyone, plus it has both a paleontologist and a leopard: seriously.
My 2 write-ins are my two favourite screwball comedies: 'His Girl Friday' and 'Arsenic & Old Lace'.
His Girl Friday has the most brilliant dialogue of classic comedy. It doesn't hurt that it has two of the greatest comedians at the top of their game. plus low-rent mafia-types, a kidnapped mother-in-law & it was directed by Howard Hawks. It is one of my two favourite films of all time. Cary and Rosalind are also my two favourite actors of classic Hollywood. Truly a master class in comedy.
Arsenic and Old Lace is the funniest film about insane serial killers ever made. This is the genius that occurs when family reunions go wonderfully wrong: a brother who believes he's Teddy Roosevelt, aunts who have a hobby of helping out older gentlemen with their elderberry wine made with arsenic, strychnine and just a pinch of cyanide and the other brother - the black sheep of the family who makes the others look down-right normal. It has a quote that I always use to describe my own relatives, "Insanity runs in my family, practically gallops!"