Well, I'm not certain it's authoritative, but a web site called
"kaput.com" seems pretty obsessive about collecting the dates for such
events, so I'll post its answer: May 18, 1934, at the Paramount. (I
presume that means the Paramount Theatre in New York City, though
there were apparently Paramount Theatres in several cities by that
time. This site's references to premieres at the "Paramount Theatre"
are each in New York City [
"This is the May 18th edition of ... D.T.'s Today In All Kinds Of
History!" (compiled 08-05-1998)
Another page, devoted to early sound films from Paramount Pictures,
states that the release date for Little Miss Marker was May 19, 1934.
"Early Paramount Sound Films 1928-1935"
This provides some confirmation for the answer, both in that the
studio was Paramount (so logically, the film would premiere at a
Paramount Theater), and in that the general release date was the
Search terms used on Google:
"little miss marker" premiered
"little miss marker" "may 18"