The Roman Hat Mystery is a novel that was written in 1929 by Ellery Queen (a pseudonym created used by Frederic Dannay and Manfred Bennington Lee).
The novel deals with the poisoning of a disreputable lawyer named Monte Field in the Roman Theater in New York City during a performance of a play called "Gunplay!"
A number of suspects are considered, but nothing can be proved until Ellery performs an extended piece of logical deduction based on the missing hat and thus identifies the murderer.
The character of Ellery Queen and the more-or-less locked room mystery format were probably suggested by the novels featuring detective Philo Vance by S.S. Van Dine, which were very popular at the time.
Though the egregious bonhomie of the Queens and Ellery's pseudo bookishness occasionally irritate, the neatness of the plot involving a missing hat in a theater murder cannot be denied.